capital markets

BUFN 740: Capital MarketsTopic 1The Investment Environment and Historical RecordBKM 1-5

Real Assets Versus Financial AssetsReal AssetsDetermine the productive capacity and net income of the economyExamples: Land, buildings, machines, knowledge used to produce goods and services

Financial AssetsClaims on real assetsThree types: Fixed income or debt, Common stock or equity, Derivative securities

BUFN 740 Capital Markets Topic 1 *

BUFN 740 Capital Markets Topic 1

Fixed IncomePayments fixed or determined by a formula

Money market debt: short term, highly marketable, usually low credit risk

Capital market debt: long term bonds, can be safe or risky



Common Stock and DerivativesCommon Stock is equity or ownership in a corporation.Payments to stockholders are not fixed, but depend on the success of the firm

DerivativesValue derives from prices of other securities, such as stocks and bondsUsed to transfer riskBUFN 740 Capital Markets Topic 1 *


Financial Markets and the EconomyInformation Role: Capital flows to companies with best prospects

Consumption Timing: Use securities to store wealth and transfer consumption to the future

Allocation of Risk: Investors can select securities consistent with their tastes for risk

Separation of Ownership and Management: With stability comes agency problems



The Investment ProcessAsset allocationChoice among broad asset classesShould you invest in stocks or in bonds and whats the optimal allocation between them?How to use futures and options to reduce risk or enhance returns?Security selectionChoice of which securities to hold within asset classWhy are some stocks more expensive than some others? Are those cheap stocks bargains? How should we evaluate securities? Their risks and their returns?BUFN 740 Capital Markets Topic 1 *


How Securities are TradedTypes of Markets:

Direct searchBuyers and sellers seek each otherBrokered marketsBrokers search out buyers and sellersDealer marketsDealers have inventories of assets from which they buy and sellAuction marketstraders converge at one place to trade



Bid and Asked PricesBid PriceBids are offers to buy.In dealer markets, the bid price is the price at which the dealer is willing to buy.Investors sell to the bid.Bid-Asked spread is the profit for making a market in a security.Ask PriceAsked prices represent offers to sell.In dealer markets, the asked price is the price at which the dealer is willing to sell.Investors must pay the asked price to buy the security.BUFN 740 Capital Markets Topic 1 *


Types of OrdersMarket Order: Executed immediatelyTrader receives current market priceA large order may be filled at multiple pricesPrice-contingent Order: Traders specify buying or selling price



Trading MechanismsDealer markets --Originally, NASDAQ was primarily a dealer market with a price quotation system

Electronic communication networks (ECNs)True trading systems that can automatically execute orders

Specialists marketsmaintain a fair and orderly marketBUFN 740 Capital Markets Topic 1 *


Buying on Margin

The margin in the account is the portion of the purchase price contributed by the investor; the remainder is borrowed from the broker.The broker charges interest for the loan.The securities purchased are used as collateral.The board of Governors of the Federal Reserve sets limits on the extent of margin purchases. Currently, the initial margin requirement is 50%.Example: An investor pays $6,000 toward the purchase of $10,000 worth of stock (100 shares at $100 per share). The initial percentage margin is 60%. If the stock price declines by 30%, the percentage margin falls to 3,000/7,000=43%.



Maintenance marginMaintenance Margin a threshold percentage margin. If the percentage margin falls below this level, the broker will issue a margin call:Require additional capital added to the margin account.Can sell the stocks without the investors consent.Example: Suppose the maintenance margin is 30%. How far could the stock fall before the investor gets a margin call?Solve: (100 P-4000)/ (100P)=0.3.The solution is P=$57.14.Conclusion: the price can fall 42.86% before a margin call is issued.Why do brokers lend loans? Should investors borrow to invest?



Short SalesOne may sell a financial asset even though he does not own it. How is it done?Borrow the asset through a broker.Sell it and deposit proceeds and margin in an account.Buy the asset in the future in the market, and return it to the lender.The borrower must pay the lender any dividend paid during the short sale.The short seller will reap a profit if the price decreases.

Is short selling good to the financial market?BUFN 740 Capital Markets Topic 1 *


Short Sale: Initial Conditions Example 3.3Dot Bomb1000 Shares50%Initial Margin30%Maintenance Margin$100Initial Price

Sale Proceeds $100,000Margin & Equity $50,000Stock Owed 1000 sharesBUFN 740 Capital Markets Topic 1 *


Example 3.3 (Contd) Dot Bomb falls to $70 per shareAssets$100,000 (sale proceeds)$50,000 (initial margin)

Liabilities$70,000 (buy shares)

Equity $80,000 Profit = ending equity beginning equity = $80,000 - $50,000 = $30,000 = decline in share price number of shares sold short



Short Sale - Margin CallSuppose the maintenance margin is 30% on short sales, how much can the stock price rise before a margin call?

($150,000* - 1000P) / (1000P) = 30%P = $115.38

* Initial margin plus sale proceedsBUFN 740 Capital Markets Topic 1 *


Arbitrage in Real LifeArbitrage: (potential) benefits without downsideRoyal Dutch and Shell:Royal Dutch (60%) and Shell (40%)=> PriceRD = 1.5*PriceS



Arbitrage in Real LifeInternet Carve-Outs3Com Sells 5% of Palm in IPO, will spin off remainder in 6 months1 share of 3Com will own 1.5 shares of PalmPPalm = $953Com should be $142P3Com = $81Value of 3Com excluding Palm = -$60Limitations to arbitrageVery few shares of Palm available to shortArbitrage was limitedMispricing persisted



Quant reviewRisk projects: The stock price of ABC is currently $100. Assume the stock price is either going to increase to $120 or decrease to $90 over the next year. In both cases the firm will pay a dividend of $5.

100GB12090BUFN 740 Capital Markets Topic 1 *


Rate of returnThe rate of return in the G state is:

The rate of return in the B state is:

In general, the rate of return is given by:

Or equivalently, by capital gains + dividend yield:



Expected Rate of ReturnThe probabilities of the G and B states are 0.4 and 0.6 respectively.The expected rate of return is

In general, if there are n possibilities of outcome, the expected rate of return is



ExampleThe price of a Google share is $465 today. The expected return is 4% per year for the next four years. If you buy a share today, how much money will you expect to have after four years?

A zero-coupon bond from General Motors will expire after one year and pay a face value of $1000. The expected return for a GM bond is 12%. How much is the price of the bond right now? BUFN 740 Capital Markets Topic 1 *


Variance of Rate of ReturnThe variance is defined as the expectation of the squared deviations from the expectation. In our case:

In general, the variance is given by:

The standard deviation is defined as the squared root of the variance. In our example:



CovarianceFor two different assets i and j, covariance measures the direction of comovement between their returns:

For example, suppose each return could take one of two values, 5% or 15%, with the following probabilities:


rirjProbability-5%-5%30%-5%15%20%15%-5%20%15%15%30%


CovarianceNotice that Notice E(ri ) = E(rj ) = 5%Now construct:

Taking the probability-weighted average gives:


ri E(ri ) rj E(rj ) (ri E(ri ) ) (rj E(rj ) )Probability10% 10% 0.010.3010% 10% 0.01 0.2010% 10% 0.01 0.2010% 10% 0.010.30


CorrelationCovariance tells us the direction of comovement but little about its strength; standardizing the covariance by standard deviations gives a unitless measure that conveys the strength of the comovement.Correlation coefficient:

In the above example, we can see Thus

Correlation satisfies What is the meaning of



Some Useful FormulasBUFN 740 Capital Markets Topic 1 *


Mean and Variance of Historical ReturnGiven a sample of T realized returns on stock q: rq1, rq2 ,rq3, ,rqT. The estimate of expected return E(rq) is given by the sample mean

The estimate of the variance of return is

Estimated standard deviation is just the square root:



Mean and Standard Deviation of S&P 500 ReturnBUFN 740 Capital Markets Topic 1 *


Excess Return and Sharpe RatioExcess return is just return minus the riskfree rate. People usually use the T-bill rate as the riskfree rate.The excess return of a risky investment in a specific period can be positive or negative.The difference between the expected rate of return on a risky asset and the risk free rate is called a risk premium.

Example: The estimated U.S. large stocks risk premium is 7.52%, and SD is 19.54%. So the Sharpe ratio is 0.0752/0.1954=0.38.



Figure 5.4 The Normal DistributionThe normal distribution with mean=10% and standard deviation=20%.With 95% chance, the next draw is within +-2 SD from the mean. With 68% chance, the next draw is within +-1 SD from the mean.BUFN 740 Capital Markets Topic 1 *


Table 5.3 Statistics from the History of Portfolio Returns, 1926-2009BUFN 740 Capital Markets Topic 1 *


Historic Returns on Risky PortfoliosReturns appear normally distributed

Returns are lower over the most recent half of the period (1968-2009)

SD for small stocks became smaller

Better diversified portfolios have higher Sharpe Ratios



Statistical Significancet-statistic is usually used for testing the null hypothesis that E(rq) = 0:

If t exceeds 1.96, then the null is rejected at the 5% significance level.In Table 5.3, the annual returns on U.S. large-cap stocks between 1926 and 2009:

The large-cap portfolio has an average return reliably different from zero.



Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000BUFN 740 Capital Markets Topic 1 The difference between Swedenand the average return across the 16 countries is 2.5%The difference between Belgiumand the average return across the 16 countries is 2.6%The t-statistic for a difference of 2.6% with standard deviation of 23% and 100 observations is 1.13

capital markets

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