Finance-Which method of portfolio selection is better, Malcolm’s or Henry’s?

| January 30, 2017

Question
Which method of portfolio selection is better, Malcolm’s or Henry’s? Which requires more effort? Are the expected rewards different for Malcolm’s method than Henry’s method? Why?
How many inputs must be estimated by Henry to assess the benefits of adding one of the three stocks recommended by headquarters? What are they?

Pick A Stock, Any Stock

Henry Li is an investment analyst in the investment services area of Soarwest Financial and assigned to Ruth Yancey’s account. As an investment advisor, Henry’s responsibilities are to make investment recommendations to clients, execute trades on their behalf, and expand the demand for Soarwest financial services by making new contacts and clients. Ruth’s account at Soarwest is a portfolio of technology stocks worth $25,000. Her aunt established the account for college tuition, which she will need next year. The overall change in equity prices over the last three year has significantly affected the stock portfolio but, given the near-term need for cash, should have its risk profile adjusted.

“Just add a stock at random,” advises Malcolm Winsor, another analyst in the same Soarwest office. “Pick a stock, any stock, and the risk of the portfolio should be lowered. Here, use my darts and throw them at the stock pages pasted on my office wall. It’s fun and the client will never know. Just don’t let Dick catch you.”

To Henry’s thinking, there has to be a better way. The risk of Ruth’s portfolio should be reduced but Ruth needs to stay in stocks for their expected return. Twenty-five thousand tuition dollars will not buy much education these days. Henry asks Malcolm to excuse him, and he calls Soarwest headquarters for their stock recommendations. Henry knows additional analysis is needed but the recommendations are a starting point.

Random diversification is diversifying without looking at the relevant investment characteristics of the selected securities. The marginal risk reduction for the portfolio gets smaller and smaller as additional securities are added. Markowitz diversification is based on the active measurement and management of portfolio risk. Markowitz diversification takes advantage of expected return and risk for individual securities and how security returns move together.

To calculate the effect of the addition of security i to the risk (standard deviation) of an existing portfolio,sold,

s2new = (wi´si)2 + (wold´sold)2 + 2´wi´wold´si,old

The variable w is the proportion of total funds allocated either to security i or the old portfolio andsi,old is the covariance between the returns of security i and the old portfolio. If securities are related only in their common response to market returns, the covariance between security i and the old portfolio can be calculated as

si,old=bi´bold´s2market

The variableb is the beta of security i or the old portfolio ands2market is the variance of market returns.

Ruth Yancey’s current stock portfolio has an average annual total return of -14.6% over the past three years, a return standard deviation of 47%, and a beta of 0.51 relative to the S&P 500 stock index. Soarwest Financial headquarters recommends Coca-Cola Company (ticker symbol KO), General Electric Company (ticker symbol GE), or Procter & Gamble Company (ticker symbol PG) on their “buy” list. Henry knows of few Internet sites that can provide the information he needs to examine the effect of adding each of these stocks to Ruth’s portfolio: .marketwatch.com/”>Data Broadcasting Company, .yahoo.com/r/”>Yahoo Finance, and .morningstar.com/”>Morningstar. Market-level data, such as for the S&P 500 stock index, could be proxied by information available for the Vanguard Index 500 Portfolio mutual fund (ticker symbol VFINX) or taken from a text on investment management, which happens to be in Henry’s office library.

Henry will recommend to Ruth that one of the three stocks be added to the portfolio by selling either 10% or 20% of the portfolio’s value and reinvesting the proceeds in the selected stock. A greater percentage could be sold if warranted but capital gains tax considerations are an important constraint. Henry seeks the stock best able to reduce Ruth’s portfolio risk without sacrificing expected return significantly. Explaining why his recommendation reduces Ruth’s portfolio risk will also be a challenge.

Henry picks up his calculator and heads for Malcolm’s office to review Markowitz diversification. Malcolm is very bright, just undisciplined. As Henry rounds the corner next to Malcolm’s office, he overhears Dick Zuckermann’s voice. “Mr. Winsor, just what do you think you’re doing to Soarwest’s wall?” Henry turns directly around and decides to gather information instead.

Questions

1. Which method of portfolio selection is better, Malcolm’s or Henry’s? Which requires more effort? Are the expected rewards different for Malcolm’s method than Henry’s method? Why?

2. How many inputs must be estimated by Henry to assess the benefits of adding one of the three stocks recommended by headquarters? What are they?

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