Investment notes Chapter 1

An investment is a current commitment of money or other resources in the expectation of reaping future benefits. An example is a stock or bond or even education. Investments can help store and transfer wealth to a later period for consumption.

A real assets are land, building, machines and knowledge of production. A financial asset is a claim on these real assets in the forms of stocks or bonds.

There are 3 types of assets; fixed income, equity and derivatives. Fixed income or debt securities promise either a fixed stream of income or a stream of income specified by a formula. A corporate bond typically provides a fixed amount of interest whilst a floating bond depends on current volatility. Fixed income securities hold various maturities. One extreme is the money market refers to debt securities that are very short term, highly liquid and generally low risk. Examples are US T-Bills or bank certificates of deposits (CDs). The other extreme is fixed income capital markets including long term securities such as Treasury bonds and bonds by federal agencies, local municipals and corporations. Bonds range from very safe such as treasury securities to very high risk such as high yield or junk bonds. These bonds can come with conventions/enforced provisions to regarding the running of the business.

Equity in a firm represents a share in ownership on the firm’s assets. They are promised any particular payment. They do receive dividends if the firm decides to pay one and have prorated ownership in the real assets of the firm. If the firm is successful the value of equity will increase. Performance of equity is directly tied to performance, this makes equity investments riskier than debt securities.

Derivatives provide payoffs that are dependent on the prices of other assets such as stocks and bonds. Derivatives are used to hedge risk or transfer risk to other parties. Derivatives are integral to the modern financial system.

Stock prices can be said to reflect investor sentiment. If a price rises it is due to investors seeing a bright future for a firm hence invests in it. This also allows the firm to raise capital easier in markets.

Markets are competitive THERE ARE NO FREE LUNCHES!!!!!!!!! This is has 2 implications. There is a risk-return trade-off. An investor cannot be sure of returns and there will always be risk but they can diversify. Higher returns require a higher risk. Or else even one would flock to low risk high return investments, driving the price upwards, and eventually drive investors away. It also must be taken into account that markets are efficient. This means that markets price all available information quickly and efficiently concerning its values. So new information immediately gets priced into the market. Another implication is on passive and active management.

The three players are firms who demand capital, households who supply capital and governments who can borrow or lend. Stock is generally held by financial intermediaries as they stand between the issuer and the owner (individual investor). Financial intermediaries help bring together those who demand and supply capital.

Investment companies, pool and manage funds arising out of economies of scale. A problem is that many households cannot afford the management, research and brokerage fees required for management, making purchasing multiple shares expensive. Mutual funds have the advantage of large scale trading and management. Participating investors are assigned a prorated share of the total funds according to the size of their investment. This gives small investors advantaged they are willing to pay for via a management fee to the mutual fund operator. Hedge funds also pool and

Investment notes invest money from various clients. But they are only open to institutional investors and wealthy investors. They are much more likely to pursue complex and higher risk strategies. They typically keep a portion of profits as part of their fees, whereas mutual funds charge a fixed fee.

Firms raise a lot of capital by selling securities such as stocks and bonds. Firms do not do this frequently. Investment bankers specialize in these activities and their cost for providing services is below a firm maintaining an in-house security issuance division. Investment banks advise corporations on the prices it can charge for the securities it issues, interest rates and so on. Investment banks market securities in primary markets, later investors can trade previously traded securities in the secondary market. The standalone investment bank model is ending as they are becoming either bankrupt, absorbed into commercial banks or became commercial banks.

Venture capitalists are investors in young companies who have not issued securities and have little access to liquidity, which can be very risky. When they invest in companies they expect equity and some or all control of the board. Effectively becoming partnerships. This is a part of a broader class of investment known as private equity.

Financial crisis due to subprime mortgages and corresponding CDOs. Subprime mortgages given freely as originators had little incentive to proceed with due diligence as long as they knew the loans could be sold to an investor who relied on the originators credit score. Also the subprime mortgages were securitized, restructured and credit was enhanced. This was done via CDO’s, credit default obligations. CDO’s were designed to concentrate the credit (i.e. risk) risk of a bundle of loans on one class of investors, whilst the rest of the investors are left relatively protected from that risk. SO when it came to mortgages a class of investors would take risk whilst the rest are not. The idea was to prioritize claims on loan repayments by dividing the pool into senior versus junior slices called tranches. Seniors tranches had the first claim on repayments from the entire pool, only after this junior tranches were paid. CDS also exploded alongside this.

Dodd-Frank Reform Act proposes reforms to mitigate risk. This is done by the act enforcing stricter rules on bank capital, liquidity and risk management. Also there is a mandate to increase transparency especially in derivatives markets. Such as standardizing CDS contracts so they can trade in central exchanges where prices can be determined in a deep market.

Chapter 2

Money markets are where short term debt securities are marketed. These allows firms to get short term liquidity easily, quickly and efficiently.

Treasury bills are government bonds and are sold to the public. The ask price is the amount you would have to pay to buy a T-bill from a dealer and the bid price is the slightly lower price if you wanted to sell a bill to a dealer. Bid-ask spread is the difference between these prices and the dealers profit. Certificate of Deposit (CD), is a time deposit with a bank at an agreed interest rate and covenants. The CD can be sold to other investors if they need cash before being paid back from the bank. They are sold in $100,000s and are insured by the Federal Deposit Insurance Corporation upto $250,000. Firms may rather issue their own short-term unsecured debt than get a loan from a bank, this is known as commercial paper.

Eurodollars are dollar deposits outside the US. They have different regulations than being deposited in the US.

Investment notes Federal funds are accounts that banks have with the Fed which have minimum requirements dependent on deposits in their bank and other regulations. If banks have excess fed funds they can lend to those with a shortage, the rate they lend at is called the fed funds rate.

Inflation protected treasury bonds, are bonds who have their principal amount linked to the CPI index.

Common stock is standard share of ownership. Preferred stock gets a fixed payment but does not get voting power. Tax treatments are also favourable.

Exchange traded funds are offshoots of mutual funds, as they allow investors to trade index portfolios just as they do shares of stock. The first ETF was SPDR (spider), Standard & Poor’s Depository Receipt which is a unit investment trust holding a portfolio matching the S&P500 index. ETF’s can be traded during the trading hours just like shares. ETF’s have become a significant portion of global AUM. Another ETF is DIAMOND or Dow Jones Industrial Average. There can also be commodity, industry and sector ETF’s.

Real interest rate is the growth of your purchasing power. Nominal interest rate is the growth rate of money.

Expected return: E(r)=∑p(s)r(s) Variance (Standard Deviation is square root): δ2=∑p(s)[r(s)-E(r)]2

Sharpe Ratio¿Risk Premiun

SDof Excess Returns . This is essentially a reward-risk ratio. Allocation of portfolio

resources between risky portfolio and risk free asset: rc= yrp + (1-y)rf. Taking expectation: rf +y[E(rp)-rf]. Hence the standard deviation of the portfolio is yδp.

Then Capital Allocation Line (CAL) is a straight line which depicts all the risk-return combination

available to investors. The slope of the line isE (rp )−rfδp

. The slope is also called the reward-to-

volatility ratio or the Sharpe Ratio. Higher ratio means a steeper line.

Market risk/Systematic risk/non-diversifiable risk is market-wide risk sources that are still present after extensive diversification. In contrast diversifiable risk is called unique risk, firm specific risk, non-systematic risk or diversifiable risk.

Portfolio return is WdRd+WeRe=Rp, where D is debt and R is equity returns. E(rp)=WdE(rd)+weE(re).

Variance of the 2 asset portfolio is δ2p=w2

D δ2D+ w2

E δ2E+2wDwECov(rD,rE), where Covariance=ρδ2

Dδ2E.

Minimum variance frontier is the part of the graph for which there is the lowest possible volatility for a given level of expected return. Individual assets lie to the right of the frontier a implying single asset portfolios are inefficient and that diversifying leads to lower volatility and higher returns. Portfolios on the frontier provide the best risk-return trade off. The part of the frontier that lies above the global minimum variance portfolio is the efficient frontier of risky assets.

CAPM

The capital pricing model is a set of predictions concerning equilibrium expected returns on assets. CAPM asks what would happen if all investors shared an identical investable universe and the saem input list. The result would be that all the frontiers would be identical. Given that they all face the same risk-free rate, then all investors draw an identical tangent CAL and arrive at the same risky portfolio with the same weights. As the market portfolio is an aggregation of all of these identical

Investment notes risky portfolios it will too have the same weights. Thus if investors choose the same risky portfolio it must be the market portfolio. The CAL based on each investors optimal risky portfolio will in fact also be the CML.

Security Market Line shows the relationship between returns and beta, also can be interpreted as risk-reward. The beta of a security is the appropriate measure of its risk because beta is proportional to the risk the security contributes to the optimal risky portfolio. Risk averse investors measure the risk of a portfolio via volatility. Thus we expect the risk premium on individual assets to depend on the contribution of that asset to the risk of the portfolio. The beta of a stock measures its contribution to the variance of the market portfolio. CAPM states that the securities risk premium is directly proportional to both beta and the risk premium of the market portfolio. That is the risk premium is equal to β[E(rm)-rf]. The expected return-beta is portrayed as the SML. The slope of the SML is E(rm)-rf. ]

Beta is a measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), a model that calculates the expected return of an asset based on its beta and expected market returns. Beta is calculated using regression analysis, and you can think of beta as the tendency of a security's returns to respond to swings in the market. A beta of 1 indicates that the security's price will move with the market. A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. For example, if a stock's beta is 1.2, it's theoretically 20% more volatile than the market. Beta can be calculated as covariance between a stock and index divided by variance of the index.

Es = rf + Bs(Emkt - rf)

Where: rf = the risk-free rate

Bs = the beta of the investment

Emkg = the expected return of the market

Es = the expected return of the investment

The CML graphs the risk premiums of efficient portfolios as a function of standard deviation. The SML graphs individual assets risk premiums as a function of asset risk. The SML provides a benchmark for the evaluation of investment performance. Given the risk of investment, as measured by beta, the SML provides the required rate of return necessary to compensate investors for risk and time value of money. Fairly priced assets thus lie on the SML in equilibrium.

Suppose SML is used as a benchmark to assess fair expected return on a risky asset. If a stock is perceived to be a good buy or under-priced it will provide an expected return in excess of the fair return stipulated by the SML. Under-priced stocks are above the SML and over priced stocks are below the SML. Given their betas, their expected returns are greater than dictated by the CAPM.

The difference between the fair and actually expected rates of return on a stock is called the stocks alpha, α.

EXAMPLE- If market return is 14%, beta=1.2 and T-bill rate is 6%. The SML would predict 6+1.2(12-6)= 15.6%. Thus if one expected a return of 17%, the implied alpha would be 1.4%.

Security analysis could be about finding non-zero alphas. This suggests that the starting point of portfolio management can be a passive market index portfolio, the manager then can decrease the

Investment notes weights of securities which have negative alphas and increase weights of securities with positive alphas. CAPM could be used to provide a required rate of return that the projects need to yield based on its beta to be acceptable to investors. Managers can use CAPM to obtain this cut-off IRR or hurdle rate for a project.

The key implications of CAPM are;

The market portfolio is efficient. The risk premium on a risky asset is proportional to its beta.

ARBITRAGE PRICING THEORY AND MULTIFACTOR MODELS OF RISK AND RETURN

Multifactor models seek to improve the explanatory power of single factor models by explicitly accounting for the various systematic components of security risk. These models use indicators intended to capture a wide range of macroeconomic risk factors.

A (risk-free) arbitrage opportunity arises when two or more security prices enable investors to construct a zero-net-investment portfolio that will yield a sure profit. The presence of arbitrage opportunities will generate a large volume of trades that puts pressure on security prices. This pressure will continue until prices reach levels that preclude such arbitrage. When securities are priced so that there are no risk-free arbitrage opportunities, we say that they satisfy the no-arbitrage condition. Price relationships that satisfy the no-arbitrage condition are important because we expect them to hold in real-world markets.

Portfolios are called “well-diversified” if they include a large number of securities and the investment proportion in each is sufficiently small. The proportion of a security in a well-diversified portfolio is small enough so that for all practical purposes a reasonable change in that security’s rate of return will have a negligible effect on the portfolio’s rate of return.

Efficient Market Hypothesis

Stock prices should follow a random walk, that is, that price changes should be random and unpredictable. Far from a proof of market irrationality, randomly evolving stock prices would be the necessary consequence of intelligent investors competing to discover relevant information on which to buy or sell stocks before the rest of the market becomes aware of that information. Don’t confuse randomness in price changes with irrationality in the level of prices. If prices are determined rationally, then only new information will cause them to change. Therefore, a random walk would be the natural result of prices that always reflect all current knowledge. Indeed, if stock price movements were predictable, that would be damning evidence of stock market inefficiency, because the ability to predict prices would indicate that all available information was not already reflected in stock prices. Therefore, the notion that stocks already reflect all available information is referred to as the efficient market hypothesis (EMH). Therefore, announcement of a takeover attempt should cause the stock price to jump. Hence, stock prices jump dramatically on the day the news becomes public. However, there is no further drift in prices after the announcement date, suggesting that prices reflect the new information, including the likely magnitude of the takeover premium, by the end of the trading day.

Why should we expect stock prices to reflect “all available information”? After all, if you are willing to spend time and money on gathering information, it might seem reasonable that you could turn up something that has been overlooked by the rest of the investment community. When information is

Investment notes costly to uncover and analyse, one would expect investment analysis calling for such expenditures to result in an increased expected return. Thus, in market equilibrium, efficient information-gathering activity should be fruitful.

The weak-form hypothesis asserts that stock prices already reflect all information that can be derived by examining market trading data such as the history of past prices, trading volume, or short interest. This version of the hypothesis implies that trend analysis is fruitless. Past stock price data are publicly available and virtually costless to obtain. The weak-form hypothesis holds that if such data ever conveyed reliable signals about future performance, all investors already would have learned to exploit the signals. Ultimately, he signals lose their value as they become widely known because a buy signal, for instance, would result in an immediate price increase. The semi strong-form hypothesis states that all publicly available information regarding the prospects of a firm must be reflected already in the stock price. Such information includes, in addition to past prices, fundamental data on the firm’s product line, quality of management, balance sheet composition, patents held, earning forecasts, and accounting practices. Again, if investors have access to such information from publicly available sources, one would expect it to be reflected in stock prices. Finally, the strong-form version of the efficient market hypothesis states that stock prices reflect all information relevant to the firm, even including information available only to company insiders. This version of the hypothesis is quite extreme. Few would argue with the proposition that corporate officers have access to pertinent information long enough before public release to enable them to profit from trading on that information.

Technical Analysis

Technical analysis is essentially the search for recurrent and predictable patterns in stock prices. Although technicians recognize the value of information regarding future economic prospects of the firm, they believe that such information is not necessary for a successful trading strategy. This is because whatever the fundamental reason for a change in stock price, if the stock price responds slowly enough, the analyst will be able to identify a trend that can be exploited during the adjustment period. The key to successful technical analysis is a sluggish response of stock prices to fundamental supply-and-demand factors. This prerequisite, of course, is diametrically opposed to the notion of an efficient market. Technical analysts are sometimes called chartists because they study records or charts of past stock prices, hoping to find patterns they can exploit to make a profit. As an example of technical analysis, consider the relative strength approach. The chartist compares stock performance over a recent period to performance of the market or other stocks in the same industry. A simple version of relative strength takes the ratio of the stock price to a market indicator such as the S&P 500 index. If the ratio increases over time, the stock is said to exhibit relative strength because its price performance is better than that of the broad market. Such strength presumably may continue for a long enough period of time to offer profit opportunities. One of the most commonly heard components of technical analysis is the notion of resistance levels or support levels. These values are said to be price levels above which it is difficult for stock prices to rise, or below which it is unlikely for them to fall, and they are believed to be levels determined by market psychology.

The efficient market hypothesis implies that technical analysis is without merit. The past history of prices and trading volume is publicly available at minimal cost. Therefore, any information that was ever available from analyzing past prices has already been reflected in stock prices. As investors compete to exploit their common knowledge of a stock’s price history, they necessarily drive stock prices to levels where expected rates of return are exactly commensurate with risk. At those levels

Investment notes one cannot expect abnormal returns. An interesting question is whether a technical rule that seems to work will continue to work in the future once it becomes widely recognized. A clever analyst may occasionally uncover a profitable trading rule, but the real test of efficient markets is whether the rule itself becomes reflected in stock prices once its value is discovered. Once a useful technical rule (or price pattern) is discovered, it ought to be invalidated when the mass of traders attempts to exploit it. In this sense, price patterns ought to be self-destructing.

Fundamental Analysis

Fundamental analysis uses earnings and dividend prospects of the firm, expectations of future interest rates, and risk evaluation of the firm to determine proper stock prices. Ultimately, it represents an attempt to determine the present discounted value of all the payments a stockholder will receive from each share of stock. If that value exceeds the stock price, the fundamental analyst would recommend purchasing the stock. Fundamental analysts usually start with a study of past earnings and an examination of company balance sheets. They supplement this analysis with further detailed economic analysis, ordinarily including an evaluation of the quality of the firm’s management, the firm’s standing within its industry, and the prospects for the industry as a whole. The hope is to attain insight into future performance of the firm that is not yet recognized by the rest of the market. Once again, the efficient market hypothesis predicts that most fundamental analysis also is doomed to failure. If the analyst relies on publicly available earnings and industry information, his or her evaluation of the firm’s prospects is not likely to be significantly more accurate than those of rival analysts. Many well-informed, well-financed firms conduct such market research, and in the face of such competition it will be difficult to uncover data not also available to other analysts. Only analysts with a unique insight will be rewarded. The trick is not to identify firms that are good, but to find firms that are better than everyone else’s estimate. Similarly, poorly run firms can be great bargains if they are not quite as bad as their stock prices suggest.

Active V Passive

By now it is apparent that casual efforts to pick stocks are not likely to pay off. Competition among investors ensures that any easily implemented stock evaluation technique will be used widely enough so that any insights derived will be reflected in stock prices. Moreover, these techniques are economically feasible only for managers of large portfolios. If you have only $100,000 to invest, even a 1% per year improvement in performance generates only $1,000 per year, hardly enough to justify herculean efforts. The billion-dollar manager, however, reaps extra income of $10 million annually from the same 1% increment. The small investor probably is better off investing in mutual funds. By pooling resources in this way, small investors can gain from economies of scale. More difficult decisions remain, though. Can investors be sure that even large mutual funds have the ability or resources to uncover mispriced stocks? Furthermore, will any mispricing be sufficiently large to repay the costs entailed in active portfolio management? Proponents of the efficient market hypothesis believe that active management is largely wasted effort and unlikely to justify the expenses incurred. Therefore, they advocate a passive investment strategy that makes no attempt to outsmart the market. A passive strategy aims only at establishing a well-diversified portfolio of securities without attempting to find under- or overvalued stocks. Passive management is usually characterized by a buy-and-hold strategy. Because the efficient market theory indicates that stock prices are at fair levels, given all available information, it makes no sense to buy and sell securities frequently, which generates large trading costs without increasing expected performance. One common strategy for passive management is to create an index fund, which is a fund designed to

Investment notes replicate the performance of a broad-based index of stocks. Exchange-traded funds, or ETFs, are a close (and often lower-expense) alternative to indexed mutual funds. As noted in Chapter 4, these are shares in diversified portfolios that can be bought or sold just like shares of individual stock.

If the market is efficient, why not pick stocks by throwing darts at The Wall Street Journal instead of trying rationally to choose a stock portfolio? This is a tempting conclusion to draw from the notion that security prices are fairly set, but it is far too facile. There is a role for rational portfolio management, even in perfectly efficient markets. You have learned that a basic principle in portfolio selection is diversification. Even if all stocks are priced fairly, each still poses firm-specific risk that can be eliminated through diversification. Therefore, rational security selection, even in an efficient market, calls for the selection of a well-diversified portfolio providing the systematic risk level that the investor wants. Rational investment policy also requires that tax considerations be reflected in security choice. High-tax-bracket investors generally will not want the same securities that low bracket investors find favourable. A third argument for rational portfolio management relates to the particular risk profile of the investor. For example, a Toyota executive whose annual bonus depends on Toyota’s profits generally should not invest additional amounts in auto stocks. To the extent that his or her compensation already depends on Toyota’s well-being, the executive is already overinvested in Toyota and should not exacerbate the lack of diversification. Investors of varying ages also might warrant different portfolio policies with regard to risk bearing. For example, older investors who are essentially living off savings might choose to avoid long-term bonds whose market values fluctuate dramatically with changes in interest rates (discussed in Part Four). Because these investors are living off accumulated savings, they require conservation of principal. In contrast, younger investors might be more inclined toward long-term inflation-indexed bonds. The steady flow of real income over long periods of time that is locked in with these bonds can be more important than preservation of principal to those with long life expectancies. In conclusion, there is a role for portfolio management even in an efficient market. Investors’ optimal positions will vary according to factors such as age, tax bracket, risk aversion, and employment. The role of the portfolio manager in an efficient market is to tailor the portfolio to these needs, rather than to beat the market.

Are Markets Efficient?

Not surprisingly, the efficient market hypothesis does not exactly arouse enthusiasm in the community of professional portfolio managers. It implies that a great deal of the activity of portfolio managers—the search for undervalued securities—is at best wasted effort, and quite probably harmful to clients because it costs money and leads to imperfectly diversified portfolios. Consequently, the EMH has never been widely accepted on Wall Street, and debate continues today on the degree to which security analysis can improve investment performance. Before discussing empirical tests of the hypothesis, we want to note three factors that together imply that the debate probably never will be settled: the magnitude issue, the selection bias issue, and the lucky event issue.

The Magnitude Issue We noted that an investment manager overseeing a $5 billion portfolio who can improve performance by only .1% per year will increase investment earnings by .001 3 $5 billion 5 $5 million annually. This manager clearly would be worth her salary! Yet can we, as observers, statistically measure her contribution? Probably not: A .1% contribution would be swamped by the yearly volatility of the market. Remember, the annual standard deviation of the well-diversified S&P 500 index has been around 20%. Against these fluctuations, a small increase in performance would be hard to detect. All might agree that stock prices are very close to fair values

Investment notes and that only managers of large portfolios can earn enough trading profits to make the exploitation of minor mispricing worth the effort. According to this view, the actions of intelligent investment managers are the driving force behind the constant evolution of market prices to fair levels. Rather than ask the qualitative question, Are markets efficient? we ought instead to ask a more quantitative question: How efficient are markets?

The Selection Bias Issue Suppose that you discover an investment scheme that could really make money. You have two choices: either publish your technique in The Wall Street Journal to win fleeting fame, or keep your technique secret and use it to earn millions of dollars. Most investors would choose the latter option, which presents us with a conundrum. Only investors who find that an investment scheme cannot generate abnormal returns will be willing to report their findings to the whole world. Hence opponents of the efficient markets’ view of the world always can use evidence that various techniques do not provide investment rewards as proof that the techniques that do work simply are not being reported to the public. This is a problem in selection bias; the outcomes we are able to observe have been preselected in favor of failed attempts. Therefore, we cannot fairly evaluate the true ability of portfolio managers to generate winning stock market strategies.

The Lucky Event Issue In virtually any month it seems we read an article about some investor or investment company with a fantastic investment performance over the recent past. Surely the superior records of such investors disprove the efficient market hypothesis. Yet this conclusion is far from obvious. As an analogy to the investment game, consider a contest to flip the most number of heads out of 50 trials using a fair coin. The expected outcome for any person is, of course, 50% heads and 50% tails. If 10,000 people, however, compete in this contest, it would not be surprising if at least one or two contestants flipped more than 75% heads. In fact, elementary statistics tells us that the expected number of contestants flipping 75% or more heads would be two. It would be silly, though, to crown these people the “head-flipping champions of the world.” Obviously, they are simply the contestants who happened to get lucky on the day of the event. (See the nearby box.) The analogy to efficient markets is clear. Under the hypothesis that any stock is fairly priced given all available information, any bet on a stock is simply a coin toss. There is equal likelihood of winning or losing the bet. However, if many investors using a variety of schemes make fair bets, statistically speaking, some of those investors will be lucky and win a great majority of the bets. For every big winner, there may be many big losers, but we never hear of these managers. The winners, though, turn up in The Wall Street Journal as the latest stock market gurus; then they can make a fortune publishing market newsletters. Our point is that after the fact there will have been at least one successful investment scheme. A doubter will call the results luck; the successful investor will call it skill. The proper test would be to see whether the successful investors can repeat their performance in another period, yet this approach is rarely taken

Behavioural Critique

The premise of behavioural finance is that conventional financial theory ignores how real people make decisions and that people make a difference. 1 A growing number of economists have come to interpret the anomalies literature as consistent with several “irrationalities” that seem to characterize individuals making complicated decisions. These irrationalities fall into two broad categories: first, that investors do not always process information correctly and therefore infer incorrect probability distributions about future rates of return; and second, that even given a probability distribution of returns, they often make inconsistent or systematically suboptimal decisions.

Investment notes Errors in information processing can lead investors to misestimate the true probabilities of possible events or associated rates of return. Several such biases have been uncovered. Here are four of the more important ones.

Forecasting Errors A series of experiments by Kahneman and Tversky 2 indicate that people give too much weight to recent experience compared to prior beliefs when making forecasts (sometimes dubbed a memory bias ) and tend to make forecasts that are too extreme given the uncertainty inherent in their information. DeBondt and Thaler 3 argue that the P/E effect can be explained by earnings expectations that are too extreme. In this view, when forecasts of a firm’s future earnings are high, perhaps due to favourable recent performance, they tend to be too high relative to the objective prospects of the firm. This results in a high initial P/E (due to the excessive optimism built into the stock price) and poor subsequent performance when investors recognize their error. Thus, high P/E firms tend to be poor investments.

Overconfidence People tend to overestimate the precision of their beliefs or forecasts, and they tend to overestimate their abilities. In one famous survey, 90% of drivers in Sweden ranked themselves as better-than-average drivers. Such overconfidence may be responsible for the prevalence of active versus passive investment management—itself an anomaly to adherents of the efficient market hypothesis. Despite the growing popularity of indexing, only about 15% of the equity in the mutual fund industry is held in indexed accounts. The dominance of active management in the face of the typical underperformance of such strategies (consider the generally disappointing performance of actively managed mutual funds reviewed in Chapter 4 as well as in the previous chapter) is consistent with a tendency to overestimate ability. An interesting example of overconfidence in financial markets is provided by Barber and Odean, 4 who compare trading activity and average returns in brokerage accounts of men and women. They find that men (in particular, single men) trade far more actively than women, consistent with the generally greater overconfidence among men well documented in the psychology literature. They also find that trading activity is highly predictive of poor investment performance. The top 20% of accounts ranked by portfolio turnover had average returns 7 percentage points lower than the 20% of the accounts with the lowest turnover rates. As they conclude, “trading [and by implication, overconfidence] is hazardous to your wealth.” Overconfidence appears to be a widespread phenomenon, also showing up in many corporate finance contexts. For example, overconfident CEOs are more likely to overpay for target firms when making corporate acquisitions. 5 Just as overconfidence can degrade portfolio investments, it also can lead such firms to make poor investments in real assets.

Conservatism A conservatism bias means that investors are too slow (too conservative) in updating their beliefs in response to new evidence. This means that they might initially underreact to news about a firm, so that prices will fully reflect new information only gradually. Such a bias would give rise to momentum in stock market returns. Sample Size Neglect and Representativeness The notion of representativeness bias holds that people commonly do not take into account the size of a sample, acting as if a small sample is just as representative of a population as a large one. They may therefore infer a pattern too quickly based on a small sample and extrapolate apparent trends too far into the future. It is easy to see how such a pattern would be consistent with overreaction and correction anomalies. A short-lived run of good earnings reports or high stock returns would lead such investors to revise their assessments of likely future performance, and thus generate buying pressure that exaggerates the price run-up.

Prospect Theory Prospect theory modifies the analytic description of rational risk-averse investors found in standard financial theory. 12 Figure 12.1, panel A, illustrates the conventional description of

Investment notes a risk-averse investor. Higher wealth provides higher satisfaction, or “utility,” but at a diminishing rate (the curve flattens as the individual becomes wealthier). This gives rise to risk aversion: A gain of $1,000 increases utility by less than a loss of $1,000 reduces it; therefore, investors will reject risky prospects that don’t offer a risk premium. Figure 12.1, panel B, shows a competing description of preferences characterized by “loss aversion.” Utility depends not on the level of wealth, as in panel A, but on changes in wealth from current levels. Moreover, to the left of zero (zero denotes no change from current wealth), the curve is convex rather than concave. This has several implications. Whereas many conventional utility functions imply that investors may become less risk averse as wealth increases, the function in panel B always re-centres on current wealth, thereby ruling out such decreases in risk aversion and possibly helping to explain high average historical equity risk premiums.

Even if information processing were perfect, many studies conclude that individuals would tend to make less-than-fully-rational decisions using that information. These behavioral biases largely affect how investors frame questions of risk versus return, and therefore make risk–return trade-offs.

Framing Decisions seem to be affected by how choices are framed. For example, an individual may reject a bet when it is posed in terms of the risk surrounding possible gains but may accept that same bet when described in terms of the risk surrounding potential losses. In other words, individuals may act risk averse in terms of gains but risk seeking in terms of losses. But in many cases, the choice of how to frame a risky venture—as involving gains or losses—can be arbitrary.

Mental Accounting Mental accounting is a specific form of framing in which people segregate certain decisions. For example, an investor may take a lot of risk with one investment account but establish a very conservative position with another account that is dedicated to her child’s education. Rationally, it might be better to view both accounts as part of the investor’s overall portfolio with the risk–return profiles of each integrated into a unified framework. Nevertheless, Statman 7 points out that a central distinction between conventional and behavioural finance theory is that the behavioural approach views investors as building their portfolios in “distinct mental account layers in a pyramid of assets,” where each layer may be tied to particular goals and elicit different levels of risk aversion. In another paper, Statman 8 argues that mental accounting is consistent with some investors’ irrational preference for stocks with high cash dividends (they feel free to spend dividend income, but would not “dip into capital” by selling a few shares of another stock with the same total rate of return) and with a tendency to ride losing stock positions for too long (because “behavioural investors” are reluctant to realize losses). In fact, investors are more likely to sell stocks with gains than those with losses, precisely contrary to a tax minimization strategy. 9 Mental accounting effects also can help explain momentum in stock prices. The house money effect refers to gamblers’ greater willingness to accept new bets if they currently are ahead. They think of (i.e., frame) the bet as being made with their “winnings account,” that is, with the casino’s and not with their own money, and thus are more willing to accept risk. Analogously, after a stock market run-up, individuals may view investments as largely funded out of a “capital gains account,” become more tolerant of risk, discount future cash flows at a lower rate, and thus further push up prices.

Regret Avoidance Psychologists have found that individuals who make decisions that turn out badly have more regret (blame themselves more) when that decision was more unconventional. For example, buying a blue-chip portfolio that turns down is not as painful as experiencing the same losses on an unknown start-up firm. Any losses on the blue-chip stocks can be more easily attributed to bad luck rather than bad decision making and cause less regret. De Bondt and Thaler 10 argue

Investment notes that such regret avoidance is consistent with both the size and book-to-market effect. Higher book-to-market firms tend to have depressed stock prices. These firms are “out of favor” and more likely to be in a financially precarious position. Similarly, smaller, less well known firms are also less conventional investments. Such firms require more “courage” on the part of the investor, which increases the required rate of return. Mental accounting can add to this effect. If investors focus on the gains or losses of individual stocks, rather than on broad portfolios, they can become more risk averse concerning stocks with recent poor performance, discount their cash flows at a higher rate, and thereby create a value-stock risk premium.

Limits to Arbitrage Behavioural biases would not matter for stock pricing if rational arbitrageurs could fully exploit the mistakes of behavioural investors. Trades of profit-seeking investors would correct any misalignment of prices. However, behavioural advocates argue that in practice, several factors limit the ability to profit from mispricing.

Fundamental Risk Suppose that a share of IBM is under-priced. Buying it may present a profit opportunity, but it is hardly risk-free, because the presumed market under-pricing can get worse. While price eventually should converge to intrinsic value, this may not happen until after the trader’s investment horizon. For example, the investor may be a mutual fund manager who may lose clients (not to mention a job!) if short-term performance is poor, or a trader who may run through her capital if the market turns against her, even temporarily. A comment often attributed to the famous economist John Maynard Keynes is that “markets can remain irrational longer than you can remain solvent.” The fundamental risk incurred in exploiting apparent profit opportunities presumably will limit the activity of traders.

Implementation Costs Exploiting overpricing can be particularly difficult. Short selling a security entails costs; short-sellers may have to return the borrowed security on little notice, rendering the horizon of the short sale uncertain; other investors such as many pension or mutual fund managers face strict limits on their discretion to short securities. This can limit the ability of arbitrage activity to force prices to fair value.

Model Risk One always has to worry that an apparent profit opportunity is more apparent than real. Perhaps you are using a faulty model to value the security, and the price actually is right. Mispricing may make a position a good bet, but it is still a risky one, which limits the extent to which it will be pursued.

BONDS!!!!!!!!!!

A bond is a security that is issued in connection with a borrowing arrangement. The borrower issues (i.e., sells) a bond to the lender for some amount of cash; the bond is the “IOU” of the borrower. The arrangement obligates the issuer to make specified payments to the bondholder on specified dates. A typical coupon bond obligates the issuer to make semiannual payments of interest to the bondholder for the life of the bond. These are called coupon payments because in precomputer days, most bonds had coupons that investors would clip off and present to claim the interest payment. When the bond matures, the issuer repays the debt by paying the bond’s par value (equivalently, its face value). The coupon rate of the bond determines the interest payment: The annual payment is the coupon rate times the bond’s par value. The coupon rate, maturity date, and par value of the bond are part of the bond indenture, which is the contract between the issuer and the bondholder. Like the government, corporations borrow money by issuing bonds. Figure 14.2 is a sample of listings for a few actively traded corporate bonds. Although some bonds trade electronically on the NYSE Bonds platform, most bonds are traded over-the-counter in a network of

Investment notes bond dealers linked by a computer quotation system. In practice, the bond market can be quite “thin,” with few investors interested in trading a particular issue at any particular time.

Some corporate bonds are issued with call provisions allowing the issuer to repurchase the bond at a specified call price before the maturity date. For example, if a company issues a bond with a high coupon rate when market interest rates are high, and interest rates later fall, the firm might like to retire the high-coupon debt and issue new bonds at a lower coupon rate to reduce interest payments. This is called refunding. Callable bonds typically come with a period of call protection, an initial time during which the bonds are not callable. Such bonds are referred to as deferred callable bonds. The option to call the bond is valuable to the firm, allowing it to buy back the bonds and refinance at lower interest rates when market rates fall. Of course, the firm’s benefit is the bondholder’s burden. Holders of called bonds must forfeit their bonds for the call price, thereby giving up the attractive coupon rate on their original investment. To compensate investors for this risk, callable bonds are issued with higher coupons and promised yields to maturity than noncallable bonds.

Convertible bonds give bondholders an option to exchange each bond for a specified number of shares of common stock of the firm. The conversion ratio is the number of shares for which each bond may be exchanged.

While the callable bond gives the issuer the option to extend or retire the bond at the call date, the extendable or put bond gives this option to the bondholder. If the bond’s coupon rate exceeds current market yields, for instance, the bondholder will choose to extend the bond’s life. If the bond’s coupon rate is too low, it will be optimal not to extend; the bondholder instead reclaims principal, which can be invested at current yields.

Floating-rate bonds make interest payments that are tied to some measure of current market rates. For example, the rate might be adjusted annually to the current T-bill rate plus 2%. If the 1-year T-bill rate at the adjustment date is 4%, the bond’s coupon rate over the next year would then be 6%. This arrangement means that the bond always pays approximately current market rates. The major risk involved in floaters has to do with changes in the firm’s financial strength. The yield spread is fixed over the life of the security, which may be many years. If the financial health of the firm deteriorates, then investors will demand a greater yield premium than is offered by the security. In this case, the price of the bond will fall. Although the coupon rate on floaters adjusts to changes in the general level of market interest rates, it does not adjust to changes in the financial condition of the firm.

International bonds are commonly divided into two categories, foreign bonds and Eurobonds. Foreign bonds are issued by a borrower from a country other than the one in which the bond is sold. The bond is denominated in the currency of the country in which it is marketed. In contrast to foreign bonds, Eurobonds are denominated in one currency, usually that of the issuer, but sold in other national markets. For example, the Eurodollar market refers to dollar-denominated bonds sold outside the United States (not just in Europe), although London is the largest market for Eurodollar bonds. Because the Eurodollar market falls outside U.S. jurisdiction, these bonds are not regulated by U.S. federal agencies. Similarly, Euroyen bonds are yen-denominated bonds selling outside Japan, Eurosterling bonds are pound-denominated Eurobonds selling outside the United Kingdom, and so on.

Bond value = Present value of coupons + Present value of par value

Investment notes

Corporate bonds typically are issued at par value. This means that the underwriters of the bond issue (the firms that market the bonds to the public for the issuing corporation) must choose a coupon rate that very closely approximates market yields. In a primary issue, the underwriters attempt to sell the newly issued bonds directly to their customers. If the coupon rate is inadequate, investors will not pay par value for the bonds. After the bonds are issued, bondholders may buy or sell bonds in secondary markets. In these markets, bond prices fluctuate inversely with the market interest rate. The inverse relationship between price and yield is a central feature of fixed income securities. Interest rate fluctuations represent the main source of risk in the fixed-income market, and we devote considerable attention in Chapter 16 to assessing the sensitivity of bond prices to market yields.

The yield to maturity (YTM) is defined as the interest rate that makes the present value of a bond’s payments equal to its price. This interest rate is often interpreted as a measure of the average rate of return that will be earned on a bond if it is bought now and held until maturity. To calculate the yield to maturity, we solve the bond price equation for the interest rate given the bond’s price. The bond’s yield to maturity is the internal rate of return on an investment in the bond.

Determinants of Bond Safety

Bond rating agencies base their quality ratings largely on an analysis of the level and trend of some of the issuer’s financial ratios. The key ratios used to evaluate safety are

1. Coverage ratios —Ratios of company earnings to fixed costs. For example, the times-interest-earned ratio is the ratio of earnings before interest payments and taxes to interest obligations. The fixed-charge coverage ratio includes lease payments and sinking fund payments with interest obligations to arrive at the ratio of earnings to all fixed cash obligations (sinking funds are described below). Low or falling coverage ratios signal possible cash flow difficulties.

2. Leverage ratio, debt-to-equity ratio —A too-high leverage ratio indicates excessive indebtedness, signaling the possibility the firm will be unable to earn enough to satisfy the obligations on its bonds.

3. Liquidity ratios —The two most common liquidity ratios are the current ratio (current assets/current liabilities) and the quick ratio (current assets excluding inventories/current liabilities). These ratios measure the firm’s ability to pay bills coming due with its most liquid assets.

4. Profitability ratios —Measures of rates of return on assets or equity. Profitability ratios are indicators of a firm’s overall financial health. The return on assets (earnings before interest and taxes divided by total assets) or return on equity (net income/equity) are the most popular of these measures. Firms with higher returns on assets or equity should be better able to raise money in security markets because they offer prospects for better returns on the firm’s investments.

5. Cash flow-to-debt ratio —This is the ratio of total cash flow to outstanding debt.

Bond Indentures

Sinking Funds Bonds call for the payment of par value at the end of the bond’s life.

Investment notes This payment constitutes a large cash commitment for the issuer. To help ensure the commitment does not create a cash flow crisis, the firm agrees to establish a sinking fund to spread the payment burden over several years. The fund may operate in one of two ways:

1. The firm may repurchase a fraction of the outstanding bonds in the open market each year.

2. The firm may purchase a fraction of the outstanding bonds at a special call price associated with the sinking fund provision. The firm has an option to purchase the bonds at either the market price or the sinking fund price, whichever is lower. To allocate the burden of the sinking fund call fairly among bondholders, the bonds chosen for the call are selected at random based on serial number.

Subordination of Further Debt One of the factors determining bond safety is total outstanding debt of the issuer. If you bought a bond today, you would be understandably distressed to see the firm tripling its outstanding debt tomorrow. Your bond would be riskier than it appeared when you bought it. To prevent firms from harming bondholders in this manner, subordination clauses restrict the amount of additional borrowing.

Dividend Restrictions Covenants also limit the dividends firms may pay. These limitations protect the bondholders because they force the firm to retain assets rather than paying them out to stockholders.

Collateral Some bonds are issued with specific collateral behind them. Collateral is a particular asset that the bondholders receive if the firm defaults on the bond. If the collateral is property, the bond is called a mortgage bond. If the collateral takes the form of other securities held by the firm, the bond is a collateral trust bond. In the case of equipment, the bond is known as an equipment obligation bond.

Bonds and interest rates sensitivity

1. Bond prices and yields are inversely related: as yields increase, bond prices fall; as yields fall, bond prices rise.

2. An increase in a bond’s yield to maturity results in a smaller price change than a decrease in yield of equal magnitude.

3. Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds.

4. The sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases. In other words, interest rate risk is less than proportional to bond maturity.

5. Interest rate risk is inversely related to the bond’s coupon rate. Prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds.

6. The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling.

Duration

Rule 1 for Duration The duration of a zero-coupon bond equals it’s time to maturity.

Investment notes Rule 2 for Duration Holding maturity constant, a bond’s duration is lower when the coupon rate is higher.

Rule 3 for Duration Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity. Duration always increases with maturity for bonds selling at par or at a premium to par.

Rule 4 for Duration Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower.

Rule 5 for Duration The duration of a level perpetuity is;

Convexity

As a measure of interest rate sensitivity, duration clearly is a key tool in fixed-income portfolio management. Percentage change in the value of a bond approximately equals the product of modified duration times the change in the bond’s yield:

Dividend discount model

It is tempting, but incorrect, to conclude from Equation 18.3 that the DDM focuses exclusively on dividends and ignores capital gains as a motive for investing in stock. Indeed, we assume explicitly in Equation 18.1 that capital gains (as reflected in the expected sales price, P 1 ) are part of the stock’s value. Our point is that the price at which you can sell a stock in the future depends on dividend forecasts at that time. The reason only dividends appear in Equation 18.3 is not that investors ignore capital gains. It is instead that those capital gains will reflect dividend forecasts at the time the stock is sold.

Adding growth we have

Investment notes Performance Evaluation

1. U.S. assets are only a part of the world portfolio. International capital markets offer important opportunities for portfolio diversification with enhanced risk–return characteristics.

2. Exchange rate risk imparts an extra source of uncertainty to investments denominated in foreign currencies. Much of that risk can be hedged in foreign exchange futures or forward markets, but a perfect hedge is not feasible unless the foreign currency rate of return is known.

3. Several world market indexes can form a basis for passive international investing. Active international management can be partitioned into currency selection, country selection, stock selection, and cash/bond selection.