Question

The (annual) expected return and standard deviation of returns for 2 assets are as follows:

Asset A : E[r] 10% , SD[r] 30%

Asset B : E[r] 20% , SD[r] 50%

The correlation between the returns is 0.15

a. Calculate the expected returns and standard deviations of the following portfolios:

i) 80% in A, 20% in B : 12%/27.35%

ii) 50% in A, 50% in B : 15% /30.02%
iii) 20% in A, 80% in B : 18%/41.33%
b. Find the weights for a portfolio with an expected return of 25%? What is the standard deviation of this portfolio?
Wa = -50%
Wb = 1.50%
74.25

----------------------------------Use those questions' answers.

In addition to the information in Q1, assume that the (annual) risk-free (T-bill) rate is 4%.

a. Calculate the expected returns and standard deviations of the following portfolios:

i) 75% in the risk-free asset, 25% in B

ii) 25% in the risk-free asset, 75% in B

iii) 50% in the risk-free asset, 50% in the portfolio in Q1 a(ii)

b. Calculate the Sharpe ratios of

(i) asset A

Iii) Asset B

III) the portfolio in Q.1a(i)

iv) the portfolio in Q, 1a(ii)

v) the portfolio in Q.1a(iii)

Answer 1

ANSWER

(a) part

(i)  Weight(Rf Asset) = 0.75 , Weight(B) = 0.25

ER(portfolio) = { ER(Rf Asset) * Weight(Rf Asset) } + { ER(B) * Weight(B) }

= { 4 * 0.75 } + { 20 * 0.25 }

= 8 %

SD(portfolio) = SD(B) * Weight(B) FORMULA of SD in case portfolio consists Rf Assets

= 50 * 0.25

= 12.5 %

(ii)  Weight(Rf Asset) = 0.25 , Weight(B) = 0.75

ER(portfolio) = { ER(Rf Asset) * Weight(Rf Asset) } + { ER(B) * Weight(B) }

= { 4 * 0.25 } + { 20 * 0.75 }

= 16 %

SD(portfolio) = SD(B) * Weight(B)

= 50 * 0.75

= 37.5 %

(iii)  Weight(Rf Asset) = 0.50 , Weight(Portfolio in Q1 aii) = 0.50

ER(portfolio) = { ER(Rf Asset) * W(Rf Asset) } + { ER(Portfolio in Q1 aii) * W(Portfolio in Q1 aii) }

= { 4 * 0.50 } + { 15 * 0.50 }

= 9.5 %

SD(portfolio) = SD(Portfolio in Q1 aii) * Weight(Portfolio in Q1 aii)

= 30.29 * 0.50

= 15.15 %

(b) part

SHARPE RATIO = (ER - Rf) / SD

(i) Asset A Sharpe Ratio = (10 - 4) / 30

= 0.2

(ii) Asset B Sharpe Ratio = (20 - 4) / 50

= 0.32

(iii) Portfolio in Q.1a(i) Sharpe Ratio = (12 - 4) / 27.35

= 0.29

(iv) Portfolio in Q.1a(ii) Sharpe Ratio = (15 - 4) / 30.29

= 0.36

(v) Portfolio in Q.1a(iii) Sharpe Ratio = (18 - 4) / 41.33

= 0.34

IF ANY DOUBT IN ANY PART PLEASE ASK IN COMMENT :)