Posted: September 16th, 2017

Pick A Stock, Any Stock

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, σold,
σ2new = (wi ×  σi)2 + (wold ×  σold)2 + 2 ×  wi ×  wold ×  σi,old
The variable w is the proportion of total funds allocated either to security i or the old portfolio
and σi,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
σi,old = βi × βold × σ2market
The variable β is the beta of security i or the old portfolio and  σ2market 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: Data Broadcasting
Company, Yahoo Finance, and 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?