5. Suppose your investment portfolio is comprised of the Russel 1000 Index ETF t

Question

5. Suppose your investment portfolio is comprised of the Russel 1000 Index ETF this index represents the 1000 largest publicly traded firms in the U.S.-with ticker IWF. You are thinking of buying one (and only one) of the following assets: stock of Tesla (ticker TSLA), stock of Best Buy (BBY), or a Treasury Bonds ETF (IEF) Your new portfolio will be coinprised of 90% IWF with the rest in the asset you buy Below are average returns, standard deviations, and correlations based on monthly returns for the past five years. Would you buy one (Note: think in terms of the Sharpe ratio, see HW1) of the three assets? If so, which asset would you buy? Explain Expected Return Standard Deviatiorn Correlations IWF TSLA BBY IEF 1.375% 1.692% 1 .988% 0.206% 3.004% 12. I 70% 9.352% 1.458% 1.00 0.27 1.00 0.25 0.03 1.00 -0.18-0.03 -0.31 1.00

Explanation / Answer

To see which asset to buy, we will use every asset as remaining 10% and calculate the Sharpe Ratio of the portfolio. Whereever Sharpe Ratio is high that option one should go with.

Please note ,

Sharpe Ratio =Expected Return - Risk Free Return / Standard Deviation,

In this formula we will use risk free return = return of IEF since the treasury yield is usually considered as risk free return.

As we now, 90% of the portfolio is IWF.

1. Lets Assume remaining 10% is also IWF. Now the Sharpe Ratio of this portfolio is,

Here, Expected return will be of IWF = 1.375%, Risk free return will be of IEF = 0.206% and Standard deviation will be of IWF = 3.004%

Sharpe Ratio for option 1 =1.375% - 0.206% / 3.004% = 0.3891

2. Lets Assume remaining 10% is TSLA. Now to calculate the portfolio return and standard deviation we will use weighted average method.

Weighted average portfolio return = (90%*1.375%)+(10%*1.692%) = 1.4067%

Standard deviation of portfolio = (90%*3.004%)+(10%*12.170%) = 3.9206%

Sharpe Ratio for option 2 is

= (1.40687%-0.206%)/3.9206% = 0.3063

3. Lets Assume remaining 10% is BBY. Now to calculate the portfolio return and standard deviation we will use weighted average method.

Weighted average portfolio return = (90%*1.375%)+(10%*1.988%) = 1.4363%

Standard deviation of portfolio = (90%*3.004%)+(10%*9.352%) = 3.6388%

Sharpe Ratio for option 3 is

= (1.4363%-0.206%)/3.6388% = 0.3381

4. Lets Assume remaining 10% is IEF. Now to calculate the portfolio return and standard deviation we will use weighted average method.

Weighted average portfolio return = (90%*1.375%)+(10%*0.206%) = 1.2581%

Standard deviation of portfolio = (90%*3.004%)+(10%*1.458%) = 2.8494%

Sharpe Ratio for option 4 is

= (1.2581%-0.206%)/2.8494% = 0.3692

From all the four options, Option 1 has the highest Sharpe Ratio i.e. Risk adjusted return. And hence the remaining 10% of portfolio should also consist of IWF.

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