Standard deviation
Choosing securities at random, form equally weighted portfolios of 2, 5, 10, 15 and 20 securities
determine the standard deviation of these portfolios and plot the standard deviations against the number
of securities in the portfolios. Comment on your results and compare these with the results of the
studies of naïve diversification.
(In undertaking this analysis you can derive the results for each of the portfolios using the Excel
spreadsheet –there is no need to employ the portfolio equations and estimates of co-variances etc.).
(Approximately 500 words)
(20 marks)
Question 2:
a. Choose any five securities at random and determine the average returns for each
company for the 132 months along with the variance and standard deviation of these
returns. Next construct an equally weighted portfolio made up of the five securities, and
determine the series of monthly returns. On this basis determine the average return for the
portfolio and the associated variance and standard deviation. Explain and discuss the
relationship between the average returns, average variance, and average standard
deviation for the five securities and the average returns, variance, and standard deviation
for the portfolio.
(10 Marks)
b. Calculate the co-variances for each pair of securities in the portfolio and on the basis of
this information, and using the relevant portfolio equations (use the equation below),
calculate the standard deviation of the returns on the portfolio. Compare your results to
those obtained for the portfolio in part a above. Comment and explain your findings.
(10 Marks)
c. Estimate the betas of the five securities you chose (in a) using the following market
model:
where:
Ri = the return on security i
RM = the return on the market index
αi = the intercept term
βi = the slope term
еi = the random residual error
Comment on what the value of the beta (the slope coefficients in the regression)
indicates. Then, determine the beta of your portfolio (use the relevant equation).
(15 Marks)
d. Discuss the primary determinants of a share’s beta. (This part of the questions relates to
betas in general and does not require you to focus on the company analysed in part (c)
(Approximately 500 words)
(15 Marks)
1 1 ( ) . (1 ) .
VAR R Av VARIANCE Av CO VARIANCE P
N N
Part II (Stock Valuation)
Question 3: Price-Earnings (P/E) ratio
i. Explain carefully what is meant by a price earnings ratio.
ii. Utilising a valuation model identify and briefly discuss the theoretical determinants of the ratio.
iii. Briefly discuss some of the other factors that might influence the value of a company’s reported P/E
ratio.
(15 marks)
Part III (Derivative Securities)
Question 4: (Options)
Options Traded on Marks & Spencer Shares
Share Price Exercise Price Market Prices of Calls Market Prices of Puts
Sep Oct Nov Sep Oct Nov
210 205 12.0 24.0 27.0 6.0 17.5 19.5
210 9.5 21.5 24.5 8.5 20.0 22.0
TOTAL100 MARKS (GOOD LUCK)
a) Explain carefully why the November calls are trading at higher prices than the September calls.
(5 marks)
b) Draw a diagram to illustrate the possible payoffs from investing a straddle, using calls and puts
expiring in November and an exercise price of 210. Explain the circumstances in which
an investor might consider it worthwhile to invest in a straddle.
c) Comment on the contention that options are a zero sum game for the writer and investor in options.
(5 marks)