Question

In: Finance

1.Suppose you have a riskless asset with a rate of return of 0.05 and a risky...

1.Suppose you have a riskless asset with a rate of return of 0.05 and a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.16. What portfolio combination of these two assets will yield an expected rate of return of 0.08? What is its standard deviation? (2 pts)

Solutions

Expert Solution

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%


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