In: Finance
Given:
Risk Less Asset | Risky asset | |
Expected return | 0.05 | 0.12 |
Standard deviation | 0 | 0.16 |
Note :
1. The returns of risk less asset do not change. Therefore, the
Standard Deviation of risk less or risk free assets = 0
2. Also, cofficient of correlation between the riskless assets and
risk assets is zero (r = 0) as return of riskless assets
has no correlation with return of risky security.
A) Calculation of portfolio combination of these two assets will yield an expected rate of return of 0.08
Expected Return of Portfolio (ERp) = 0.08
Let the weight of riskless asset be X
Weight of Risk less asset = 1 - X
ERp = ERa*Wa + ERb*Wb
where ERa & ERb = Return of Risk less asset & risky asset
respectively
Wa & Wb = Weights of Risk less asset & risky
asset respectively
0.08 = 0.05*X + 0.12*(1-X)
0.08 = 0.05X + 0.12 - 0.12X
-0.04 = - 0.07X
x = 0.571429 or 57.14%
Weight of riskless asset = 57.14 %
Weight of risky asset = 1 - 0.5714 = 0.4286 or 42.86%
B) Calculation of Standard Deviation
where
= Standard Deviation of Risk less asset & risky asset
respectively
Wa & Wb = Weights of Risk less asset & risky
asset respectively
r = cofficient of correlation
We know that r = 0 &
. Therefore,
0.068576 or 6.86%
Standard Deviation = 6.86%