MGTB09H3 – Principles of Finance
Additional selfstudy exercises topic 6 – Risk Return Analysis
answers at the end
Question 1 (Risk and Return)
Given the following information on a portfolio of 3 stocks held by Asif Thakor:
Economy Probability Roeturn Reotfurn Rotfurn
Bust 0.25 0.00 -0.35 -0.95
a. If Asif’s portfolio is invested 30% in Mei Wa, 50% in Man-Lei, and 20% in Masair, what is
the portfolio expected return? The variance? The standard deviation?
b. If the expected T-Bill rate is 5%, what is the expected risk premium on the portfolio?
c. If the expected inflation rate is 2%, what is the expected real return on the portfolio? What is
the expected real risk premium on the portfolio?
d. What is the required rate of return on the portfolio, if the market risk premium is 7%, and
portfolio beta is 1.6?
Question 2 (Risk and Return)
Following is the historical cash dividend and price data on Aaron Kam & Yeon Kim Systems
(AYS) and Nhi La & Eric Leung Enterprises (NEE) stocks:
Aaron Kam & Yeon Kim Systems Nhi La & Eric Leung Enterprises
Year Dividend Price YearividendPrice
1993 $--- $40.00 1993 $--- $15.00
a. Calculate the yearly rate of returns for AYS and NEE stocks, and a portfolio comprised of
40% invested in AYS stock and 60% invested in NEE stock.
b. Calculate the mean rate of returns and standard deviations for AYS stock, NEE stock and the
portfolio. Suppose the risk free rate is 4%. Calculate the Sharpe ratios of both stocks and that
of the portfolio. What is your conclusion based on these Sharpe ratios?
Question 3 (Risk and Return)
The expected returns for two firms, A and B are as follows:
State of Economy Probability Return of Firm A Return of Firm B
1 0.1 -0.05 -0.10
2 0.40.10 0.15
3 0.30.25 0.10
4 0.20.30 0.18
Firm A has total investment in assets of $75,000,000; three times that of Firm B. Assume that a
new firm, C, is formed through a merger between Firms A and B. The share of A and B in the
portfolio represented by Firm C is based on the ratio of their total assets prior to the merger.
a. Calculate the expected return and standard deviation of Firm A and B before the merger.
b. Calculate the expected return and standard deviation of Firm C.
c. Based on risk/return, which firm will, you invest in? And why? (Assume the risk free rate is
Question 4 (Risk and Return)
Lisa Harvey & Fanny Lam Ltd. (LFL) and Yousuf Talal & Jessica Wu Inc. (YJI) stocks have the
following historical dividend and price data:
Year Dividend Year-end Pric e DividendYeaP rined
0 --- $22.50 --- $43.75
1 $2.00 16.00 $3.40 35.50
a. Calculate the realized rate of return for each stock in each year. Then assume that someone
held a portfolio that was half LFL stock half YJI stock. What was the realized rate of return
on the portfolio in each year from year 1 through year 5? What are the average returns for
each stock and for the portfolio?
b. Calculate the standard deviation of returns for each stock and for the portfolio.
c. Based on the extent to which the portfolio has a lower risk than the stocks held individually,
would you guess that the correlation coefficient between returns on the two stocks is closer to
0.9, 0.0, or –0.9?
d. If you add more stocks at random to the portfolio, what is the most accurate statement of
what happens to σ p
1. σp remains constant.
2. σp declines to approximately 15%
3. σp declines to zero if enough stocks are included.
Answer 1 (Risk and Return)
a. First, calculate the expected portfolio return in each of the three possible future states of
BoEo(r : ) = 0.3(0.3) + 0.5(0.45) + 0.20(1.35) = 0.585
Normal:E(r p) = 0.3(0.2) + 0.5(0.25) + 0.2(0.45) = 0.275
BuEs(:r p) = 0.3(0) + 0.5(-0.35) + 0.20(-0.95) = -0.365
Next, calculate the portfolio expected return, taking the probabilities of the future states
of the economy into account:
E(R p) = 0.35(0.585) + 0.4(0.275) + 0.25(-0.365) = 0.2235
Note that we can also calculate Ep by first calculating the expected return for the three
individual stocks and then taking a weighted sum (using the portfolio weights) to
calculate the portfolio expected return.
σ 20.35(0.585-0.2235) 2+0.40(0.275-0.2235) +0.25(-0.365-0.2235) = 0.1334
σ p = 0.3652
b. RP p= E(R