FINANCIAL MANAGEMENT

Financial Management

Financial Management

Question 24-2

Solution

Security A

Security B

Expected rate = 6%

Expected rate = 11%

Standard Deviation = 30%

Standard Deviation = 10%

Correlation with the market = _ 0.25

Correlation with the market = 0.75

Beta coefficient = _ 0.5

Beta coefficient = 0.5

Answer

Security A is more risky than Security B, because the standard deviation of Security A is higher than security B (30%>10%) (Brigham, 2011).

Justification

Standard deviation is a statistical measure of the variability of a distribution. An analyst may wish to calculate the standard deviation of historical returns on a stock or a portfolio as a measure of the investment's riskiness. The higher the standard deviation of an investment's returns, the greater the relative riskiness because of uncertainty in the amount of return (Brigham, 2011). Analysts calculate the standard deviation by taking the average return earned by an asset over a measurable period of time and then computing the magnitude of variations around that average. The larger the variations, the larger the standard deviation (and hence the more risk).

Question 24-8

Solution

Requirement A

Stock Y

Market

3

4

18.2

14.3

9.1

19

(6)

(14.7)

(15.3)

(26.6)

33.1

37.2

6.1

23.8

3.2

(7.2)

14.8

6.6

24.1

20.5

18

30.6

Correlation

0.88

Standard deviation

13.76

19.64

Mean

9.85

9.77

Beta

0.774

Requirement B

The regression line and the beta coefficient show that stock Y has positive and linear relationship the market portfolio. Therefore, the return on stock Y moves with market movement. The value of beta 0.774 infers that if market gives a return of 1 dollars then stock Y will give return of 0.774 dollar (on every 100 dollar investment).

Requirement C

The firm's risk if the stock is held in a one-asset portfolio

If the scattered point would be more spread in above given graph then the risk of firm would increase as it only invests in one asset portfolio. The distance of scattered point from the regression line show the dispersion of return from the mean of return- this dispersion is known as standard deviation- more the dispersion more the risk in investing in stock and vice versa.

The actual risk premium on the stock if the CAPM holds exactly

The actual risk premium will increase because the risk premium depends on the risk in the asset.

Requirement D

If the regression line were downward sloping and beta was negative then:

Stock Y's return would be expected to have the opposite sign of NYSE return, and would be especially valuable as a diversifier

The relationship between market return and stock Y return would be inverse. Therefore, the market move positively and give positive return then Stock Y provide us with negative return and moves negatively.

The risk premium on the stock would remain same as the magnitude of the beta remains same (.774).

Key concepts

Understanding Risk and Return

We start the analysis by assuming a single-period economy, starting at Date 0 and ending at Date 1. For simplicity, we refer to Date 0 as today and Date 1 as tomorrow. The  analysis can easily be extended to multiple periods, but the simplified valuation framework considered here is sufficient for deriving the general asset pricing results.

A representative 1 investor living in our simplified economy is faced with the problem of choosing how much of his or her wealth he or she will ...