A peer of yours (who has not yet taken thin elm asked you for investment advice.

Question

A peer of yours (who has not yet taken thin elm asked you for investment advice. They want to accumulate wealth for retirement, are risk arose, and do not really complement the concept of the efficient set. Your peer would like to put all of their assets into a single low risk money market fund. Show them low moving a potion of their investment into a riskier asset will actually DECREASE their risk while INCREASING their returns. They want to ingest everything in the Vanguard Inflation-Protected Securities Fund; Investor (YIPSX) Fund which, over the last three-year period, had a standard donation of 4.36 and a return of .88%. You are suggesting that they put a portion of their portfolio mot a riskier investment, perhaps the Fidelity Real Estate Investment Portfolio (FRESX), which, over the last three-year period, had a standard deviation of 13.41 and a return of 12.98%. Assume that the future performance of these funds will match the poor three-year Pen rod, and that the correlation between the funds is 0.160. "What is the expected annual return and binders deviation of investing everything in YIPSX? Can you calculate a portfolio weighting at which the expected return will be higher than a 100% investment in VIPSX? What are the weightings, the expected annual return, and the standard deviation of that portfolio? How will you explain what this means to your peer?

Explanation / Answer

1. As the future performance will match the prior 3 year period, the future annual return of 100% investment in VIPSX = the prior return for the 3 year period = 0.88%

2. Future standard deviation will also be the same as the prior 3 year period if 100% investment is made in VIPSX = 4.36%

3. Let the weight of VIPSX be "x". Weight of FRESX = 1-x. expected return = weight of VIPSX*return of VIPSX+ weight of FRESX*return of FRESX = x*0.88%+(1-x)*12.98%.

Now, the portfolio return > 0.88%

Thus, x*0.88%+(1-x)*12.98%>0.88%

or 0.88%*x+12.98%-12.98%*x>0.88%

or 12.1%>12.1%*x

or 1>x

Thus x should be less than 100%. It could be any ratio like 99% in VIPSX and balance 1% in FRESX or 90% in VIPSX and 10% in FRESX.

The portfolio that i have created is 99% investment in VIPSX and 1% investment in FRESX.

4. Expected return of the portfolio = weight of VIPSX*return of VIPSX+ weight of FRESX*return of FRESX

= 0.99*0.88% + 0.01*12.98%

= 1.001%

5. Portfolio's standard deviation = [(weight of VIPSX)^2*(standard deviation of VIPSX)^2 + (weight of FRESX)^2*(standard deviation of fresx)^2 + (2*weight of VIPSX*weight of FRESX*standard deviation of VIPSX*standard deviation of fresx*correlation]^1/2

= (0.99^2*4.360^2+0.01^2*13.410^2+2*0.99*0.01*4.360*13.410*0.160)^1/2

= 4.34%

6. The above standard deviation is less than the standard deviation of 4.360% (i.e. when the entire amount is invested in VIPSX). This means that diversification leads to a reduction in risk.

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