historical data showing that the average annual rate of return on the SAP 500 po
ID: 2822586 • Letter: H
Question
historical data showing that the average annual rate of return on the SAP 500 portfolio over the past 80 years has averaged roughly 8% more than Treasury bill retum,nd hat the S&P; 500 standard deviation has been about 20% per year. Assume these values are representative of investors' expectations for future performance and that the current T-bill rate is 5%. Calculate the expected returnm and variance of portfolios invested in T-bills and the S&P; 500inde with weights as follows: (10 points) Wells 0.2 0.4 0.8 1.0 1.0 0.8 0.6 0.2 characteristics of stocks 4 and B are given as follows: are many stocks in the security market and that the that it is possible to borro ossible to borrow at the risk-free rate., rs What mus Suppose uasst Think about constructing a risk-free portfolio from stocks Ad int : Think about constructing a risk-free portfolio from -1, risk-free ra (10 points) stocks A and of theExplanation / Answer
The answer for the question no 4:
The formula for Expected Return is as follows:
E(R) = w1R1 + w2Rq + ...+ wnRn
where the weights are defined as
The weights for T Bills is 5% and the weight of S & P 500 index is 8% more than T Bills therefore it is 5%+8%=13%
W1 =weights for the T bills and S& P 500 index (1st weight)
W2 =weights for the T bills and S& P 500 index(2nd Weight )
and similarly for the rest 3 weights
Therefore E(R)=0*.05+1*.13+.2*.05+.8*.13+.4*.05+.6*.13+.8*.05+.2*.13+1*.05+0*.13
=.458
The variance is calculated as :
T Bills
Scenario Deviation from Expected Return Sqaured
1 (.1-.458) .128
2 (.104-.458) .1253
3 (.078-.458) .1444
4 (.04-.458) .1747
5 (.05-.458) .1664
Then variance is 0*.128+.2*.1253+.4*.1444+.8*.1747+1*.1664
=.6144
The standard deviation of S& P 500 is given as 20% ie .2 so the variance is .04
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.