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You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%, what proportion ofyour $1,000 investment should be invested into theriskyasset and what proportion into the Treasury bill if you want your portfolio to have an expected value of $1,100 in 1 year? What will be the resulting standard deviation of your complete portfolio?

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Answer:

The rate of return on the risky asset is 16% and on treasury bill is 6% and we need a return of (1100-1,000)/1000= 10% or 0.1

If we think of x as the percentage investment in risky asset and 1-x as the investment in non risky asset we can mathematically find what proportion we need to invest in each asset to get this return.

16x+ 6(1-x)=10

16x+6-6x=10

10x=4

x=4/10

x= 0.4

This equation tells us that we should invest 40% in risky assets and 1-x which is 60% in treasury bills. We can test our answer by putting these values and see if the return is 10 %

(0.4*16)+(0.6*6)= Rate of return

Rate of return=10%

10% of 1000 = 100

100+1000=$1100

Explanation:

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