Question

14.

In a universe with just two assets, a risky asset and a risk-free asset, what is the slope of the Capital Allocation Line if the Expected return of the risky asset is 6.22% and the standard deviation of the returns of the risky asset is 23.4%. The return on the risk-free asset is 3.21%  

Report 2 decimals.

17. An investment opportunity has 4 possible outcomes. The possible returns in each of these outcomes are -7.1%, 0.1%, 4.8% and 14.6%. If each of these outcomes is equally likely, what is the risk (as measured by the population standard deviation) of this investment? Provide the answer as a % with 1 decimal rounded off. If your answer is 3.56%, just enter/type "3.6".

Answer 1

SOLUTION 14

Given that,

Return of risky assets (R₁) = 6.22%

Standard deviation of risky assets (SD₁) = 23.40%

Risk free return ( R₂) = 3.21%

Assuming equal amount invested in both type of securities i.e., 50% in risky assets and 50% in risk free assets .

Therefore,

Return of the portfolio = R₁* W₁ + R₂* W₂

= 6.22 * 0.5 + 3.21 * 0.5

= 3.11 + 1.605

= 4.715%

Standard deviation of    = SD₁ * W₁ ( Since standard deviation of the risk free assets is zero )

the portfolio    = 23.40 * 0.5

= 11.70 %

Slope of CAL = Return of portfolio - Risk free return / Standard deviation of portfolio

= 4.715 - 3.21 / 11.70

= 1.505 / 11.70

= 0.13

SOLUTION 17

Returns(R)	Probability(P)	R - ER	(R - ER )2
- 7.1	0.25	-10.2	104.04
0.1	0.25	-3	9
4.8	0.25	1.7	2.89
14.6	0.25	11.5	132.25

Expected return of the investment ( ER) = 0.25 (-7.1 + 0.1 + 4.8 + 14.6 )

= 0.25 * 12.4

= 3.1

Variance of portfolio = 0.25 (104.04 + 9 + 2.89 + 132.25 )

= 0.25 * 248.18

= 62.045

Standard deviation of the portfolio = (62.045 )^1/2

= 7.9 %