historical data showing that the average annual rate of retu

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 the

Solution

The answer for the question no 4:

The formula for Expected Return is as follows:

E(R) = w₁R₁ + w₂R_q + ...+ w_nR_n

_{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