# Investment Management Harvard Case Solution & Analysis ## Investment Management Case Solution

Part (a)

From the following results, it is analysed that the market risk premium shows how the returns will generate the outcome of the considerations excluding the risk-free rate. It is expected that, the annual risk premium will be 0.22% if the investors will not consider to invest in a risk-free T-bills. The annual percentage indicates that the market is safe against the risk of loss when any investor will not involve to receive the risk-free rate.

The total annual variance under the case will be 0.18% and is consider to be the same in the future. So in order to assess the deviation among the returns, variance will extract into the square root value for generating the net value of standard deviation. Therefore, the annual deviation shows that there is some risk for the investment due to the moderate level of fluctuations among the prices.

Part (b)

 Part 2 Covariance Matrix MKT-RF RF MKT-RF 0.002032622 -5.02657E-06 RF -5.02657E-06 1.70928E-06 Weights Returns MKT-RF 0.5 0.32% RF 0.5 0.10% Total 1 Risk-Free rate 0.10% Risk Aversion (A) 4 Expected Return 0.21% Standard Deviation 2.25% Sharp Ratio 0.0978 Optimal Weight (W) 1.22%

For analysing the optimal weight of a portfolio for investors, some factors will be considered to find the net results in order to provide accurate information to particular investors and make recommendations of whether to invest in a portfolio or not.

First of all, the covariance matrix is identified to assess the constant changes among the market and the selected portfolio. So it has been identified that, this function can add to generate the optimal results against the connection between market and particular stock.

The second factor to include for generating the optimal results will be the weights assigned to each portfolio in order to assess the expected outcome coming from the investment process. Both indexes will grant the same weights for analysing the change in the optimal value. The average risk free rate is calculated by generating the annual rate from 2000 to 2015 under the RF stock. The risk average is estimated to be 4, which shows less risk in the investment proposal.

The net expected return of the two portfolios is calculated by relating the weighted average value per case with the annual returns. The net result will adjust the risk and return in a combination with the selected portfolios. Net standard deviation is calculated by relating the total of covariance matrix with the selected weights.

After determining all the factors associated with generating the optimal weights, it is identified that the new weight of the investment in the portfolio is somehow related to the risk factor because of the moderate level of returns under volatility factor. If the aversion risk will decrease, then there will be no risk involved in the investment. However, this optimal value illustrates the increase in the net weight from start to end. This shows that investor is likely to take positive decisions regarding the holding of stocks in the long term in order to get high optimal weights.

Part (c)

 Part 3 Standard Deviation under 100% Equity 4.51% Standard Deviation under 100% Risk-Free 0.13% Variance under 100% Equity 9.02% Variance under 100% Risk-Free 0.26% Optimal Weight (100% Equity) 0.89% (Investable wealth) Optimal Weight (100% Risk-Free) 9.62% (Investable wealth)

If considering the investment in a single portfolio, then the generating values will provide different results according to the change rate of each return under each portfolio. For example, the RF is considered to be less in the standard deviation, this means that the annual return will not fluctuate in a great number. Therefore, the optimal weights will definitely increase due to risk-free in nature...............

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