Case study

Josephine

Josephine has just landed her first job out of graduate school.  She is lucky enough to be working for one of the Big Four, earning $50,000 per year.  She expects her salary to increase by 3% each year.  Josephine has a goal of retiring after 30 years and then traveling the world in retirement for 20 years.  Once she retires she will move all of her assets into Treasury Bonds earning 2%.  Josephine would pay for her post retirement lifestyle by drawing $82,000 each year from her 401K.  She will contribute 18% of her salary to the 401K each year.  Her 401K offers her the choice of low-risk bonds yielding 5% a year indefinitely and a stock portfolio that is considerably more risky, but expected to yield 9% per year on average. 

Design a long-term portfolio, with appropriate weighting between bonds and stocks, for Josephine that will achieve her goal of allowing her to draw $82,000 a year from her 401K each year for 20 years beginning 30 years from now.  You should construct a portfolio that would produce an "expected outcome" that gives her just what she needs (i.e., $82,000 a year for 20 years with nothing left at the end) with the minimum degree of risk possible.  For simplicity, assume that whatever portfolio you develop for her would be the same portfolio for the 30 pre-retirement years. 

What is the minimum rate of return that she would require?  You can use a trial-and-error approach or use Excel's Goal-Seek function.  What proportion of her portfolio should be in low-risk bonds and what proportion should be in stocks? 

Jim

Jim is a 59-year old carpenter.  He wants to retire next month on his 60th birthday.  He will receive an annual pension of $35,000 from his former employment.  He also has a tax deferred annuity (401k) currently valued at $250,000.  At the moment, his 401k is invested in just two stocks: He is 25% invested in Microsoft (MSFT), and 75% invested in McDonald's (MCD). 

Jim has calculated the beta of both stocks (relative to the S&P 500), the standard deviation of both stocks, and the covariance of the returns of the two stocks.  He has also checked the risk-free rate and he has estimated the return on the S&P 500.  His estimates are below.

                   Stock         Beta           Standard Deviation

                   MSFT       1.8                      68%                     

                   MCD         1.3                      46%   

Correlation (MSFT, MCD) =   0.0350

Risk-free rate = 1%

Expected return on the S&P 500 = 9%

A. Estimate the expected return on his current portfolio.

Estimate the risk associated with his current portfolio in terms of both the portfolio beta and the portfolio standard deviation.

B. Limited to the two stocks that Jim is already invested, develop a better portfolio for Jim.  That is, change the weighting on Jim's two stocks to try to get a higher expected return or a lower level of risk (as measured by the standard deviation).  You can use a trial-and-error approach or use Excel's Solver function.