Given the following information about the market $r_m = 18$ per cent, $r_f = 6$ per cent, $\sigma_m = 30$ per cent.
(a) Calculate the slope of the capital market line (CML).
(b) Calculate the expected return for three mutual funds, namely, Aries (σ = 15 per cent), Taurus (β = 18
$\,$ per cent), Gemini (σ = 24 per cent).
$\,$ State the assumptions necessary for the application of the model.

Question

Given the following information about the market [latex]r_m = 18[/latex] per cent, [latex]r_f = 6[/latex]per cent, [latex]\sigma_m = 30[/latex] per cent.
(a) Calculate the slope of the capital market line (CML).
(b) Calculate the expected return for three mutual funds, namely, Aries (σ = 15 per cent), Taurus (β = 18
[latex]\,[/latex] per cent), Gemini (σ = 24 per cent).
[latex]\,[/latex] State the assumptions necessary for the application of the model.

Accepted Answer

(a) Slope of CML [latex]= r_m – r_f /\sigma_m =[/latex] 18% – 6%/30% = 0.4
(b) [latex]Assumption[/latex]: All mutual funds are efficient portfolios, otherwise
[latex]\,[/latex] security marked line rather than capital market line should be used.
[latex]\,[/latex] Expected rate = Intercept + Slope × Standard deviation
[latex]\qquad \qquad \qquad= r_f + [(r_m – r_f)/\sigma_m] \sigma_{\rho}[/latex]

$Expected\>return$	$Mutual\>fund$
6% + 0.4 × 15% = 6% + 6% = 12%	Aries
6% + 0.4 × 18% = 6% + 7.2% = 13.2%	Taurus
6% + 0.4 × 24% = 6% + 9.6% = 15.6 %	Gemini

Question 9.RQ.27: Given the following information about the market rm = 18 per......

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