FUNDAMENTALS OF FINANCE

Fundamentals of Finance

Fundamentals of Finance

Q2: Portfolio

You are considering making an investment in one or both of two securities X and Y, and you are given the following information.

Security Possible rate of return %

Probability of occurrence

X

30%

0.3

25%

0.4

20%

0.3

Y

50%

0.2

30%

0.6

10%

0.2

(a) Calculate the expected return for each security separately and for a portfolio comprising 60% X and 40% Y, assuming no correlation between the possible rates of return from the shares comprising the portfolio.

Solution

By using a Weighted Average - Expected Rate of Return (ERR) we can calculate expected return for each security:

Probability

Times

Outcome

Equals

Result

X

0.3

x

30%

=

9%

0.4

x

25%

=

10%

0.3

x

20%

=

6%

 

 

Total

25%

Probability

Times

Outcome

Equals

Result

Y

0.2

x

50%

=

10%

0.6

x

30%

=

18%

0.2

x

10%

=

2%

Total

30%

After calculating Weighted Average Expected Rate of Return (ERR), we will apply the given condition on the result:

S. No:

Security

Condition

ERR

Portfolio

1

X

60%

25%

15%

2

Y

40%

30%

12%

Total

27%

(b) Calculate the risk of each security separately and of the portfolio as defined above. Measure risk by the standard deviation of returns from the expected rate of return.

An estimator for s sometimes used is the standard deviation of the sample, denoted by sn and defined as follows:

Standard Deviation for Security A

sn = 0.098

Standard Deviation for Security B

sn = 0.020

3. Risk and Return

(a)Given the following information for the stock of Foster Company, calculate its beta.

Current price per share of common stock £50.00

Expected dividend per share next year £3.00

Constant annual dividend growth rate 9%

Risk-free rate of return 7%

Return on market portfolio 10%

Formula

Where:

KE = firm's cost of equity

RF = risk-free rate (the rate of return on a "risk free investment", e.g. U.S. Treasury Bonds)

RM = return on the market portfolio

Solution

0.15 = 0.07 + Be (0.10 - 0.07)

0.15 - 0.07 = 0.03Be

0.08 = 0.03Be

Or,

Be = 0.08/0.03

Be = 2.66

Calculating Ke from Constant Growth Rate Formula

P0 = D1/ (Ke - g)

50 = 3/ (Ke - 0.09)

Ke - 0.09 = 3/50

Ke - 0.09 = 0.06

Ke = 0.06 + 0.09

Ke = 0.15

Ke = 15%

Where,

P0 = Current price per share of common stock = £50.00

D1 = Expected dividend per share next year = £3.00

g = Constant annual dividend growth rate = 9% = 0.09

RF = Risk-free rate of return = 7% = 0.07

RM = Return on market portfolio = 10% = 0.10

(b) Explain the determinants of required returns.

Conventional finance theory posits that a positive relationship exists between the risk of an investment and the return required by the investor. Thanks to diversification, the overall risk of a diversified VC portfolio will not be as high as the average of its individual investments. The return required for a less diversified portfolio of investments should thus ...