BE300 FINANCE CLASS 3 RISK AND RETURN

BE300 Quantitative Methods and Finance

Class 3 Risk and Return

1. A share of stock of Beta Plc is selling for £50. A financial analyst summarises the uncertainty about the rate of return on the stock by specifying three possible scenarios:

Business condition
End-of-year price
Annual dividend
High growth
£68
£2.5
Normal growth
£54
£1.5
No growth
£45
£0.5

Assuming all three scenarios are equally likely, calculate:

a) the expected holding-period return;
b) the variance and standard deviation of the holding-period return;
c) the expected return and standard deviation of a portfolio invested 35% in Beta Plc and 65% in Treasury bills. The return on the bill is 5%.

2. Consider an investment in a broad portfolio of stocks (e.g., an index fund), which we will refer to as “stock market”. If the probability distribution of Holding Period Return (HPR) on the stock market is as follows:

State of the economy
Scenario
Probability
HPR (%)
Boom
1
0.3
50
Normal growth
2
0.4
18
Recession
3
0.3
-30

Calculate:
a) the expected return (or mean return) on the investment;
b) the variance and standard deviation of the holding period return
c) the expected return and standard deviation of a portfolio invested 3/4 in the stock market and 1/4 in Treasury bills. The return on bills is 5.5%.

3. Assume that you manage a risky portfolio with an expected return of 17% and a standard deviation of 23%. The T-bill rate is 4%.

a) Your client chooses to invest 60% of a portfolio in your fund and 40% in a T-bill. What is the expected return and standard deviation of your client’s portfolio?

b) Suppose your risky portfolio includes the following investments in the given proportions: Stock A
35%
Stock B
20%
Stock C
30%
Stock D
15%

What are the investment proportions of your client’s overall portfolio, including the position in T-bills?

c) What is the reward-to-variability ratio (S) of your risky portfolio and your client’s overall portfolio?

d) Draw the CAL of your portfolio on an