Expected return
Standard deviation
Er
Stock fund (s) 18 %
47 %
Bond fund(B) 7 % 41
%
T=bills rate (Rf) = 5.7 %
Correlation between stock and bond fund
0.17
Covariance (CoV SB) = r * σS * σB
0.17 * 47*41 = 327.59
Weight of stock=
( Er S - Rf) * σB^2 - [ (Er B - Rf) * Cov SB ]
_______________________________________________
(Er S - Rf)*σB^2 + [Er B - Rf) *
σS^2 - [ (Er S - Rf +ErB-Rf)* Cov SB
[(18-5.7) *
(41)^2 ] - [ (7-5.7) * 327.59)
_______________________________________________
[ (18-5.7) * (41)^2] + [ (7-5.7) *
(47)^2] - [ (18-5.7+7-5.7) * 327.59]
20250.433 /
19092.776
So, weight of S =
106.06%
weight of B =
-6.06%
Expected return = (weight of S * Expected return of S) + (Weight of
B * Expected retun of B)
(106.06%*18)+(-6.06%*7)
= 18.67 %
So, expected retun of portolio is 18.67%
Standard deviation formula
(σp) = ( (wS * σS ) ^2 + (wB * σB ) ^2 + (2 * wB* wS*σB
*σS* rSB) )^(1/2)
=
((106.06%*47)^2+(-6.06%*41)^2+(2*106.06%*-6.06%*47*41*0.17))^(1/2)
= 49.49 %
So, Standard deviation of portfolio is 49.49%.
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