Determine which fund Coppa should recommend to Stephenson, and justify your choi

Question

Determine which fund Coppa should recommend to Stephenson, and justify your choice by describing (and calculating) how your chosen fund best meets both of Stephenson’s criteria. In addition, as part of the analysis, be sure to calculate the beta of each potential fund relative to the existing portfolio and use this to find the Treynor ratio for each fund (assuming a 0% riskfree rate).

Stephenson, age 35 and single, is a surgeon. Stephenson has accumulated a $2.0 million investment portfolio that has a large concentration in small capitalization U.S. equities. After further evaluation, Stephenson's financial advisor, Carolyn Coppa, has summarized the distribution of Stephenson's current $2.0 million portfolio, which is as follows: Percent Expected of Total Annual Return 4.6% 12.4% 16.0% 3.80 1.6% 195% 29.9% 23.1% Short Temm $200,000 S600,000 Small Cap Equities $1200.000 10% 30% 60% 100% Domestic Large Cap Equities Domestic Small Total Portfolio ,000,000 Stephenson also expects to receive an additional S2.0 million and plans to invest the entire amount in an index fund that best complements the current portfolio. Coppa is, therefore, evaluating four index funds that represent different asset classes not substantially represented in the current portfolio. Coppa plans to evaluate the index funds on their ability to produce a portfolio that will meet the following two criteria relative to the current portfolio: (1) maintain or enhance expected return and (2) maintain or reduce volatility. The characteristics of the four funds Coppa is evaluating are as follows: Index Fund Fund A Fund B Fund C Fund D Expected Annual Return 15% 11% 16% 14% Expected Annual Standard Deviation 25% 22% 25% 22% Correlation of Returms with Current Portfolio +0.80 +0.60 +0.90 +0.65 Determine which fund Coppa should recommend to Stephenson, and justify your choice by describing (and calculating) how your chosen fund best meets both of Stephenson's criteria. In addition, as part of the analysis, be sure to calculate the beta of each potential fund relative to the existing portfolio and use this to find the Treynor ratio for each fund (assuming a 0% risk- free rate).

Explanation / Answer

We know that,

Beta of portfolio=

(standard deviation of portfolio * correlation of returns with current portfolio) / standard deviation of market

Now putting figures in above equation, we calculate beta of each index as follows:-

Index Fund

Equation

Beta

Fund A

(.25*.80) / .231=

0.866

Fund B

(.22*.60) /.231 =

0.571

Fund C

(.25*.90) /.231 =

0.974

Fund D

(.22*.65) /.231 =

0.619

Now ,

Treynor ratio = (Expected Annual Return - risk free rate) / beta of Index Fund

Here, Question specified that Risk free rate is equal to Zero(0%).

Index Fund

Equation

Ranking

Fund A

(15-0) / .866 =17.32

3

Fund B

(11-0) /.571 =19.26

2

Fund C

(16-0) /.974 =15.584

4

Fund D

(14-0) /.619 =22.617

1

Recommendation:- Higher treynor ratio of index fund indicates higher the return. Therefore, on the basis of above analysis ,we recomend to choose fund D to Coppa because treynor ratio of fund D is higher than other index fund.

Index Fund

Equation

Beta

Fund A

(.25*.80) / .231=

0.866

Fund B

(.22*.60) /.231 =

0.571

Fund C

(.25*.90) /.231 =

0.974

Fund D

(.22*.65) /.231 =

0.619

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