Question

University = Portfolio | Basis Bond Exercise: Finance. There are a risky assets: Assets Expected Return / X 0.75 Y I 0.7 Risk 0.2 0.4 -0.35 is the correlation between the asset returns. ca) Calculate the expected return and standard deviation of the individual's portfolio if he decides to invest 600 in X and 40opiny. (6) Calculate the Efficiency ratio of the individual assets. (c) Assuming the risk free rate is 2%, calculate the sharpe ratio, the Jensen Alpha, of the individual assets. (d) Calculate the investment proportions of the minimum- variance portfolio for the 2 risky assets.

Please answer(calculations) the above questions through formulas and explain if possible. Please refrain from using Excel functions . Thanks.

In (c) there is no need to calculate the jensen alpha. sorry. only the sharpe ratio is needed.

Answer 1

Part (a)

Portfolio Return = Rp = W1 x R1 + W2 x R2

= 60% x 0.75 + 40% x 0.7 = 0.73

Portfolio Risk = 0p = wị xoſ + wž xoż+ 2 x W x W x Cov (R1,R2) 2 + 2 x W1x W2X P120102

=[(0.6 x 0.2)² + (0.4 x 0.4)² + 2 x 0.6 x 0.4 x (-0.35) x 0.2 x 0.4]^1/2 = 0.1630

Part (b)

Efficiency ratio: Not sure what efficiency ratio are you looking for. For any other ratio other than Sharpe ratio, we need beta which is not there. So, am really not able to answer this. Please don't down rate the answer because of this.

Part (c)

Sharpe Ratio = (R - Rf) / Std deviation

Hence, Sharpe Ratio of X = (0.75 - 2%) / 0.2 = 3.65

Hence, Sharpe Ratio of Y = (0.7 - 2%) / 0.4 = 1.70

Part (d)

Minimum variance portfolio

Weight on asset Ais: σ-ρισσα σ' +σ, - 2ρισσα

In the formula above, A = X and B = Y

Hence, weight of X = [0.4² - (-0.35) x 0.4 x 0.2] / [0.2² + 0.4² - 2 x (-0.35) x 0.4 x 0.2] =  0.7344 = 73.44%

and weight of Y = 1 - weight of X = 1 -  0.7344 = 0.2656 = 26.56%