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BFF5040 Tutorial Questions

Question based on week 1 topic due in week 2

T1Q1

You are attempting to formulate an investment strategy. On the one hand, you think there is great upward potential in the stock market and would like to participate in the upward move if it materializes. However, you are not able to afford substantial stock market losses and so cannotrun the risk of a stock market collapse, which you think is also a possibility. Your investmentadviser suggests a protective put position: Buy both shares in a market index stock fund and putoptions on those shares with 3-month expiration and exercise price of $780. The stock index fund is currently selling for $900. However, your uncle suggests you instead buy a 3-month call option on the index fund with exercise price $840 and buy 3-month T-bills with face value $840.

a. On the same graph, draw the payoffs to each of these strategies as a function of the stock fund

value in 3 months. (Hint: Think of the options as being on one “share” of the stock index fund, with the current price of each share of the fund equal to $900.)

b. Which portfolio must require a greater initial outlay to establish? (Hint: Does either portfolio

provide a final payout that is always at least as great as the payoff of the other portfolio?) c. Suppose the market prices of the securities are as follows:

Stock fund $900

T-bill (face value $840) $810 Call (exercise price $840) $120 Put (exercise price $780) $ 6

Make a table of the profits realized for each portfolio for the following values of the stock price in 3 months: ST = $700, $840, $900, $960.

Graph the profits to each portfolio as a function of ST on a single graph. d. Which strategy is riskier? Which should have a higher beta?

e. Explain why the data for the securities given in part (c) do not violate the put-call parity

relationship. T1Q2

a. Which type of order is often used together with short sales (sales of securities you don?t own

but have borrowed from your broker) to limit potential losses from the short position?

i. Limit orders ii. Price-contingent orders iii. Stop-loss orders iv. Stop-buy orders v. Market orders

b. Consider the following limit-order book for a share of stock of a specialist. The last trade in

the stock occurred at a price of $50.

Limit Buy Orders Limit Sell Orders Price Shares Price Shares 49.75 500 50.25 100 49.50 800 51.50 100 49.25 500 54.75 300 49.00 200 58.25 100 48.50 600 i. If a market buy order for 100 shares comes in, at what price will it be filled? ii. At what price would the next market buy order be filled? iii. If you were a security dealer, would you want to increase or decrease your inventory

of this stock?

T1Q3

a. Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40

per share. She borrows $4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. i. What is the margin in Dée?s account when she first purchases the stock? ii. If the share price falls to $30 per share by the end of the year, what is the remaining

margin in her account? If the maintenance margin requirement is 30%, will she receive a margin call?

iii. What is the rate of return on her investment?

b. Old Economy Traders opened an account to short sell 1,000 shares of Internet Dreams from

the previous problem. The initial margin requirement was 50%. (The margin account pays no interest.) A year later, the price of Internet Dreams has risen from $40 to $50, and the stock has paid a dividend of $2 per share. i. What is the remaining margin in the account? ii. If the maintenance margin requirement is 30%, will Old Economy receive a margin

call?

iii. What is the rate of return on the investment? T1Q4

(Review key equations BKM 10Chapter 5 page 162)

Suppose your expectations regarding the stock price are as follows: State of the market Probability Ending Price Boom 0.35 140 Normal growth 0.30 110 Recession 0.35 80 Compute the mean and standard deviation of the HPR on stocks T1Q5

a. Investment management is far more tractable when rates of return can be well approximated

by the normal distribution because: i. The normal distribution is symmetric

HPR 44.5% 14% -16.5% The normal distribution belongs to a special family of distributions characterised as “stable”

iii. Scenario analysis is greatly simplified iv. Statistical dependence of returns across securities can be summarized in a

straightforward fashion

v. All of the above

b. Which of the following statement is correct?

i. When the distribution of returns is positively skewed, the standard deviation

underestimates risk

ii. When the distribution of returns is negatively skewed, the standard deviation

underestimates risk

iii. When a distribution is “skewed to the right”, its skewness measure is negative iv. When a distribution is “skewed to the right”, its skewness measure is positive v. (i) and (iii) are correct vi. (ii) and (iv) are correct

c. Which of the following statement is incorrect?

i. Kurtosis concerns the likelihood of extreme values on either side of the mean at the

expense of a smaller likelihood of moderate deviations

i. Kurtosis measures the degree of fat tails ii. Standard deviation will overestimate the likelihood of extreme events when the tails

of a distribution are fat

iii. Kurtosis of a normal distribution is defined as zero, and any kurtosis above zero is a

sign of fatter tails.

ii.

Question based on week 2 topics due in week 3

T2Q1

Suppose the rate of return on short-term government securities (perceived to be risk-free) is about 5%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model:

a. What is the expected rate of return on the market portfolio?

b. What would be the expected rate of return on a stock with a beta of 0?

c. Suppose you consider buying a share of stock at $40. The stock is expected to pay $3 dividends next year and you expect it to sell then for $41. The stock risk has been evaluated at beta=-0.5. Is the stock overpriced or under-priced? T2Q2

Suppose a market expected return of 10% and a riskless rate of 6%. Assume the CAPM.

a) A stock has correlation of 0.8 with the stock market, standard deviation of 30%, and the market standard deviation is 20%. Compute the stock's expected return.

b) Assume both borrowing and lending are possible at the riskless rate. Show how an investor can achieve a portfolio with 1.0 beta by

i. only taking positions in a riskless security and a portfolio with beta 0.8; ii. only taking positions in a riskless security and a portfolio with beta 1.5.

c) A stock has an expected return of 4%. Compute the beta of the security and argue for or against holding a position in the security. T2Q3

Assume an arbitrary two-factor APT model. The riskless rate is 4%. The expected return on a risk factor, namely Q, is 10%, and the expected return on another risk factor, R, is 12%.

a) Compute the expected return of portfolio S, which has a factor beta of 0.5 on Q and 0.75 on R. b) If portfolio S had an expected return of 12%, construct an arbitrage strategy which has no exposure to either risk factor but guarantees you a profit. State the assumptions required. T2Q4

A security analyst is in the process of measuring the cost of capital of XYZ shares. He has collected the following monthly data for the period from 2000-2005 (60 months):

rit= 60 observations of the returns on the XYZ shares over the 60-month period (one each month) rMt= 60 observations of the returns on the S&P 500 index over the sample period (one each month) rft= 60 observations of the risk-free rate (one each month) The CAPM equation is estimated through the following regression:

?????????????=????+???? ????????????? +??????

The result of the regression is presented as follow:

SUMMARY OUTPUTRegression StatisticsMultiple R0.5471493R Square0.2993723Adjusted R Square0.2872925Standard Error0.0534458Observations60ANOVAdfRegressionResidualTotal15859SSMSFSignificance F0.07079120.07079124.78296.07853E-060.1656742240.0028560.236465423InterceptMRPCoefficientsStandard Errort StatP-valueLower 95%Upper 95%Lower 95.0%Upper 95.0%0.01017460.0069004741.4744740.14576-0.0036382280.023987372-0.0036382280.0239873721.11352860.2236790044.9782446.1E-060.6657864411.5612707890.6657864411.561270789 Where Intercept = ai , MRP = rMt- rft, eit = error term

a. Read and interpret the meaning of the above regression outcome:

? What is the value of adjusted R-square and what does the figure tell us about the

overall fit of the regression model?

? Comment on the statistical significance of the Intercept and MRP ? Interpret the meaning of the coefficient of the variable MRP

b. Sample averages of the three variables are as followed: ????= 0.49% ,?? ??= 0.44% per

month.Calculate the expected excess return for XYZ share using the CAPM equation estimated above. T2Q5

The expected return-beta relationship represented in CAPM is tested through a two-stage procedure: first-pass and second-pass regression. Carefully read BKM 10 Chapter 13 p415 – 417 and answer the following questions:

a. State the first pass regression. What are the inputs and outputs of the first-pass regression? b. State the second pass regression. What are the inputs and outputs of the second-pass

regression?

c. If the empirical SML is too flat, how accurate is CAPM in predicting the performance of

high- or low- beta stocks?

d. What is the implication of a coefficient on γ2 being positive and statistically significant? e. What are the limitations of this approach? T2Q6

Identify and briefly discuss three criticisms of beta as used in the capital asset pricing model (CAPM) T2Q7