Investment and Portfolio Management BAO3403

Assignment Semester 2 2013

Nahulan Sreethararaj 3886641 Mathew Berkery 3891369 Stewart Louden 3801726 Shiraz Patel 3798548

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Solutions

1. Use the price data in Exhibit 1 for the Market index, Lorton Ltd,

Truganina Ltd, Wonders Ltd and Woods Ltd to calculate the holding-

period returns for the 24 months ending June 2013.

The holding-returns for the respective companies over the 24 month period is

as follows:

Market index (points)

Lorton Ltd

Truganina Ltd

Wonders Ltd

Woods Ltd

($) ($) ($) ($)

Jun-11 July 0.0394 0.0377 -0.0128 -0.1083 0.0688 August -0.0116 0.0382 0.1272 0.0449 -0.2163 September -0.1458 -0.0792 -0.0440 -0.0805 -0.2464 October 0.0624 0.3152 0.2340 -0.2179 0.1464 November 0.0803 -0.0040 0.0616 0.0796 0.1990 December 0.0591 -0.0715 -0.0409 0.0691 0.0632 Jan-12 0.0564 0.2032 0.0694 0.2134 0.2168 February 0.0410 0.3665 0.3397 -0.0728 -0.0723 March 0.0029 -0.1988 0.0556 0.0134 0.0158 April 0.0024 0.0205 0.0105 0.0624 0.0613 May 0.0379 0.0076 -0.0792 0.2776 0.3165 June -0.0250 -0.1639 -0.2432 0.0265 -0.0016 July 0.0544 0.0743 0.1061 0.0190 0.0184 August -0.0320 0.1049 0.1049 -0.3808 -0.3810 September -0.0063 0.1940 0.1940 -0.0151 -0.0159 October -0.0286 -0.1434 -0.1434 0.0830 0.0830 November 0.0625 -0.0402 -0.0402 0.0968 0.0973 December 0.0191 0.0715 0.0715 -0.0239 -0.0232 Jan-13 0.0578 0.1860 0.1860 -0.0847 -0.0870 February -0.0509 -0.2463 -0.2463 0.3169 0.3196 March -0.0201 0.0617 0.0617 0.0984 0.0978 April 0.0967 0.3217 0.3217 0.2745 0.2755 May -0.0308 -0.0706 -0.0706 -0.3248 -0.3254 Jun-13 -0.0219 -0.1396 0.0199 0.0579 0.1247 Total return for the 24-month period (%) 29.95 84.56 104.32 42.44 73.49

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2. Calculate the average monthly holding-period return and standard

deviation of the returns for the Market index, Lorton Ltd, Truganina

Ltd., Wonders Ltd and Woods Ltd using the data provided in exhibit 1.

The average monthly return for the respective stocks is calculated by dividing

the return for the 24-month period by the number of periods (24):

Total return over 24-months 29.95 84.56 104.32 42.44 73.49 Total return/24 1.25 3.52 4.35 1.77 3.06

Standard deviation is calculated by finding the square root of variance. Taking

the square root of the following formula will yield the standard deviation

calculation:

variance formula

The expected return is taken from the benchmark, the Market Index. The

Market Index achieved a return of 1.2478% per month over the 24 month

period. Using this data, the variance of each stock in each month was

calculated by taking the sum of the square of each stock’s monthly return

minus the expected return, which was the Market Index return. The monthly

calculations are detailed in the appendix. The square root of the final values

are taken to calculate the standard deviation:

Month Market index (points)

Lorton Ltd

Truganina Ltd

Wonders Ltd

Woods Ltd

($) ($) ($) ($)

Variance over the period 0.0662 0.6472 0.5402 0.6685 0.7983 STANDARD DEVIATION 0.2573 0.8045 0.7350 0.8176 0.8935

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3. Assume that your team has decided to invest equally in the securities

of these four companies. Calculate the monthly holding-period returns

for your four-share portfolio. (The monthly return for the portfolio is the

average of the four shares’ monthly returns.)

The monthly holding-period returns for the share portfolio is as follows:

Month Portfolio Return

Jun-11 July -0.0037

August -0.0015 September -0.1125 October 0.1194 November 0.0841 December 0.0050 Jan-12 0.1757 February 0.1403 March -0.0285 April 0.0387 May 0.1306 June -0.0956 July 0.0545 August -0.1380 September 0.0892 October -0.0302 November 0.0284 December 0.0240 Jan-13 0.0501 February 0.0360 March 0.0799 April 0.2984 May -0.1979 Jun-13 0.0157

The average monthly holding period return for the portfolio is calculated by the

sum of the weighted monthly averages of each individual stock: = (0.25* 3.523465957) + (0.25* 4.346874698) + (0.25* 1.768186842) + (0.25* 3.062233895) = 3.18% per month

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4. Calculate the standard deviation of the asset portfolio comprised of

Lorton Ltd, Truganina Ltd, Wonders Ltd and Woods Ltd shares.

Assume equal weightings of each share within the portfolio. What

happens to total risk when you combine shares into a portfolio?

The standard deviation of the asset portfolio is calculated by the sum of the

weighted standard deviations of each individual stock in the portfolio as

follows:

SDPORTFOLIO =

(0.25*SDLORTON LTD) + (0.25*SDTRUGANINA LTD) + (0.25*SDWONDERS LTD) +

(0.25*SDWOODS LTD)

Using the calculated values shown in the appendix, the standard deviation

(SD) of the portfolio is calculated as follows: = (0.25*0.8045)+(0.25*0.7350)+(0.25*0.8176)+(0.25*0.8935) = 0.81

Theoretically, when you combine shares into a portfolio, the overall risk

should decrease. The aim of diversification is to reduce unsystematic risk

(that is, the risk that is unique to an individual asset) so that primarily

systematic risk remains.1 Systemic risk can be defined as the variability of

risky assets caused by macroeconomic factors. 2 It cannot be diversified

away.3

Adding additional shares to a portfolio smoothes out unsystematic risk so that

the positive performance of some shares neutralises the negative

performance of others.4 However, the benefits of diversification hold only if

the shares in a given portfolio are not perfectly correlated.5

1 FK Reilly and KC Brown, Investment Analysis and Portfolio Management (10th ed, 2012) 212. 2 Ibid. 3 Ibid 213. 4 <http://www.investopedia.com/terms/d/diversification.asp> at 8 October 2013. 5 Ibid.

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5. Use the numbers in Exhibit 1 to determine the systematic risk (Beta) of

Lorton Ltd, Truganina Ltd, Wonders Ltd and Woods Ltd.

Beta is calculated using the following formula:

Beta Lorton Ltd

Beta Truganina Ltd

Beta Wonders Ltd

Beta Woods Ltd

1.635756137 1.339326575 0.701618957 1.654598819

6. Which measure, standard deviation or beta is used for analyzing stocks

that are placed in a diversified portfolio?

Standard deviation is a statistical measurement which is used to calculate an investment's volatility in terms of its returns.6 It is based on historical data and can be used to gauge the expected volatility of an investment in the future.7 Stable blue-chip stocks will generally have a lower standard deviation than riskier stocks.8 The beta co-efficient is used to calculate the level of a stock's systematic risk, or volatility, compared to a market portfolio.9 A stock with a beta of 1 is expected to move equal to the market, while a beta of less than 1 indicates that a stock will be less volatile than the market.10 If a stock's beta is 1.3, it is theoretically 30% more volatile than the market.11 In terms of analysis of stocks in a diversified portfolio, beta is more effective than standard deviation as it eliminates unsystematic risk and measures a security's correlation with the market as a whole.

6 <http://www.investopedia.com/terms/s/standarddeviation.asp> at 8 October 2013. 7 Ibid. 8 Ibid. 9  FK Reilly and KC Brown, Investment Analysis and Portfolio Management (10th ed, 2012) 216.  10 <http://www.investopedia.com/terms/b/beta.asp> at 8 October 2013. 11 Ibid.

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7. Use the capital asset pricing model to calculate the required rate of

return for Lorton Ltd, Truganina Ltd, Wonders Ltd and Woods Ltd. Use

the Treasury notes data in exhibit 1 to determine an annual average for

the risk-free rate of return.

RFR+B(MR-RFR)

Lorton Ltd

= 0.059125+1.6358(0.1497-0.059125)

= 0.2073

Truganina Ltd

= 0.059125+1.3393(0.1497-0.059125)

= 0.1804

Wonders Ltd

= 0.059125+0.7016(0.1497-0.059125)

= 0.1227

Woods Ltd

= 0.059125+1.6546(0.1497-0.059125)

= 0.2090

8. Using the required rates of return calculated in question 7 above and

the historical dividend information in exhibit 2, calculate the intrinsic

value for Lorton Ltd, Truganina Ltd, Wonders Ltd and Woods Ltd. Use

an annual compounded average rate of return when calculating the

historical growth rate in dividends.

ER=D1/k-g

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Lorton Ltd

g= [(2.50/2.15)^1/7] -1 ER= 2.5545/(0.2073-0.0218)

g= 0.0218 = 13.7709

D1= (2.50*1.0218)

D1= 2.5545

Truganina Ltd

g= [(1.50/1.20)^1/7] -1 ER= 1.5486/(0.1804-0.0324)

g= 0.0324 ER= 10.4635

D1= (1.50*1.0324)

D1= 1.5486

Wonders Ltd

g= [(2.80/2.50)^1/7] -1 ER= 2.8456/(0.1227-0.0163)

g= 0.0163 ER= 26.7444

D1= (2.80*1.0163)

D1= 2.8456

Woods Ltd

g= [(2.85/2.20)^1/7] -1 ER= 2.9574/(0.2090-0.0377)

g= 0.0377 ER= 17.2644

D1= (2.85*1.0377)

D1= 2.9574

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Part Two Question 1 The term “margin”, when used in the context of the futures market, has a meaning that is distinct from the way the same term is used in reference to the stock market.12 Futures contracts are an obligation to either buy or sell an underlying asset at a specified date in the future.13 Traders of futures contracts do not receive or pay the full value of the contract at the time of the trade.14 As the full payment is not made until the delivery date, futures exchanges require both the buyer and the seller to post collateral, or margin, to protect against the possibility of default.15 This initial “good faith” deposit, also called a performance bond, can be in the form of cash, bank guarantees, shares or government securities, and is held in the exchange’s clearing house until the delivery date.16 The margin funds are “marked to market” (that is, adjusted for contract price movements) at the end of each trading day to ensure that both end users maintain sufficient collateral to guarantee the successful completion of the contract.17 The minimum-level margin is set by the futures exchange and is generally 5% to 10% of the futures contract.18 Margin amounts are continuously reviewed and can be raised at times of high market volatility.19 Upon completion of the futures contract, the performance bond is refunded, plus or minus any gains or losses which occurred over the span of the contract.20 In contrast to the futures market, when the term “margin” is used in the context of the stock market, it refers to where borrowed money is used to purchase securities.21 When investors purchase stock they can pay with cash, or they can potentially borrow a portion of the cost, thereby “leveraging” the transaction.22 Leverage is achieved by buying on margin, meaning that the investor pays for the stock

12 <http://www.investopedia.com/university/futures/futures4.asp> at 3 October 2013. 13 <http://www.asx.com.au/products/futures-margins.htm> at 3 October 2013. 14 Ibid. 15 FK Reilly and KC Brown, Investment Analysis and Portfolio Management (10th ed, 2012) 78. 16 Ibid 744. 17 Ibid 744, 785. 18 Investopedia, above n 1. 19 Ibid. 20 Ibid. 21 Ibid. 22 Reilly and Brown, above n 4, 113.

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with some cash and borrows the rest (through a broker or bank) using the stock as collateral.23 After the initial purchase, changes in the market price of the stock will result in changes to the investor’s equity, which is calculated by subtracting the amount borrowed from the market value of the collateral stock.24 If the stock price increases, the investor’s equity as a proportion of the total market value of the shares also increases.25 Conversely, if there is a drop in stock prices, equity reduces. To protect against the possibility of negative equity, margin lenders will only lend a certain proportion of the overall investment amount.26 This initial margin requirement (or loan to value ratio – LVR) can vary according to the lender.27 If example, if a margin loan's maximum LVR is 80%, borrowing to invest in $20,000 worth of shares, will require a 20%, or $4,000 deposit. In addition to the initial margin requirement, there is also a maintenance margin which is an investor’s minimum required equity in proportion to the total value of their stock portfolio.28 The maintenance margin protects the lender in the event that share prices fall and the investor’s portfolio value falls below a certain point.29 If this happens, the account is considered to be “under-margined” and the investor will receive a margin call, that is, a request to provide more equity.30 The purchase of shares via leveraging is risky because margin loans not only magnify investment gains, but they also magnify losses if the stock market falls.31 Question 2 Hedging, in broad terms, is a technique used to try to offset the volatility of an investment position with another. For the purpose of investments, the objective of creating a hedge is to create a position that can offset the price of another ‘more fundamental holding’.32 As such, Herb will be concerned about price risk affecting the value of the portfolio in his control. If the market falls, so too will the value of his investments, affecting shareholder wealth. To try to reduce the potential losses in a falling market, Herb will take a position in the futures market that will allow him to profit from the falling market. Herb will sustain a loss in the fundamental holding, the stock portfolio, however by selling futures contracts of the same magnitude as the holding, he will realize a profit in the futures market. It is hoped that the profit earned in the futures 23 Ibid. 24 Ibid. 25 Ibid. 26 <http://www.ratecity.com.au/margin-loans/articles/margin-loans-australia> at 3 October 2013. 27 Ibid. 28 Reilly and Brown, above n 4, 115. 29 Ibid. 30 Ibid. 31 <http://www.leveraged.com.au/products/margin_loan.asp> at 3 October 2013. 32  Reilly and Brown, above n 4, 767  

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trade will offset the loss in the stock market; if it does cover the loss, it is known as a perfect hedge. In attempting to neutralize exposure to price risk, Herb must also take on the risk that the market may move in the opposite direction. Given the current conditions and Herb’s concern that the market may fall, he is expected to create a short hedge, done so by taking a short futures position (selling) against a long position (buy) in the stock market (in this case, to hold the stocks and not sell them). The following table summarizes the possible outcomes33: Economic event Actual stock exposure Desired hedge exposure Stock value FALL Loss Gain Stock value RISE Gain Loss In the case that the market rises, Herb will enjoy a gain in the value of his stock holdings. This gain will, however, be offset somewhat by a loss in the futures market, as the value of the futures contracts will be less than the market value of the portfolio is represents (i.e. Herb will receive less for the futures contract than the stocks are worth in the market). Such a hedging strategy does potentially reduce the upside, or the overall potential return of a portfolio. This is a necessary ‘evil’ in attempting to limit the costly effects of losses incurred in a falling market. While the hedging strategy does act as a ‘parachute’ of sorts as the market is on the way down, it also does burden the portfolio on the way up. This would be of particular concern for those who involve in hedging as speculators, however, as an investor, it may be necessary to incur the loss of a particular hedging strategy, which would be offset by the rise in stock prices (and thus negate the upside of rising prices), if there is particular concern that real and absolute losses may be incurred in a falling market.

33  ibid