An investor has $250,000 to invest in mutual funds. She has selected 33 funds for possible investment. In addition, a Federal money market fund is available for holding cash reserve. Table 7.22 gives the following data for each fund based on their 6-year performance, during 2002–2007:

i. Name of fund ii. Ticker symbol iii. Type of fund: capitalization size (small, medium, large), strategy

(value, growth, blend) or foreign iv. Average annual return (%)

v. Market risk (Beta)

Assume that any money not invested in the mutual funds can be deposited in a money market fund that will yield 3% interest at zero risk. Even though the investor is primarily interested in “growth” of her portfolio, she has the following investment restrictions:

i. No more than $25,000 should be invested in any one fund (does not apply to the money market fund).

ii. Between 15% and 30% of her total investment should be in “Mid Cap” funds.

iii. No more than 70% of her investment should be in “Large Cap”

and “Mid Cap” funds.

iv. At least 35% should be invested in “Large Cap” funds.

v. Investment in “International” funds should not exceed 30%.

vi. No more than 20% should be invested in “Small Cap” funds.

vii. Maintain a minimum cash reserve of $15,000 in the money market fund.

Questions

a. Develop the expressions for portfolio return and portfolio Beta risk.

b. Formulate a single-objective linear program (LP) for determining the optimal investment portfolio under the following criteria:

– Maximize portfolio return only

– Minimize portfolio risk only

c. Solve each of the LP problems formulated in part (b). Write down the optimal portfolios and their corresponding risk and return.

Determine the ideal solution and the bounds on return and risk.

d. Formulate and solve the LP problems to determine the optimal portfolios that will provide the minimum risk, under a portfolio return of at least R%, where R varies between the bounds obtained in part

(c) (vary R in increments of 2%). Plot a graph of return versus risk and identify the efficient portfolios.

e. Based on the results in part (d), what will be your recommended portfolio?

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TABLE 7.22 Performance Data on Mutual Funds (2002-2007) Fund Name Allianz NFJ Small Cap Value American Funds Amcap American Funds EuroPac American Funds Fundamental BlackRock Equity Calamos Growth Columbia Acron USA DFA US Small Cap Fidelity Nordic First Eagle Fund of America Frankling Bal Sh Investment Gabelli Equity Income GMO Emerging Markets GMO Foreign Small Co Harbor International Inv Janus Sm Value Legg Mason Emerging Market Legg Mason Intl Eq Finint Legg Mason P Aggr Grow Longleaf Partners Sm-Cap Lord Abbet Small Cap MainStay MAPA Marshall Mid Cap Val Adv Mass Mutual Prem Intl Navellier Mid Cap Growth Oakmark International Old Mutual Mid Cap T. Rowe Price New Horiz Van Kempen Growth & Income Vanguard Euro Stock Victory Diversified Stk Waddell & Reed Adv Intl WF Advanced Common Stk Ticker PCVAX AMPCX AEPGX ANCFX MADVX CVGRX LAUAX DPSTX FNORX FEAMX FCBSX GCAEX GMOEX GPSFX HIINX JSCVX LGEMX LGFEX SHRAX LLSCX LRSCX MAPAX MVEAX MMIAX NPMDX OAKIX OAMIX PRNHX ACGIX VEURX SRVEX UNCGX SCSAX Type Small cap value Large cap growth International Large cap blend Large cap value Large cap growth Small cap growth Small cap blend International Mid cap blend Mid cap value Large cap value International International International Small cap value International International Large cap growth Small cap value Small cap blend Large cap blend Mid cap value International Mid cap growth International Mid cap blend Small cap growth Large cap value International Large cap blend International Mid cap blend Average Annual Return 16.66 9.57 18.43 14.45 14.13 12.59 14.72 14.80 23.41 12.82 14.55 13.62 33.48 26.74 21.07 11.22 31.88 19.77 13.01 17.59 18.52 14.01 13.94 16.36 10.34 17.38 13.00 15.29 12.12 18.64 1241 13.23 15.37 Beta Risk 1.13 0.92 0.98 1.01 0.82 1.68 1.25 1.56 1.42 0.89 1.09 0.8 1.46 1.06 1.12 1.07 1.65 1.04 1.24 0.99 1.44 1.1 1.05 1.14 1.49 0.83 1.3. 1.48 0.86 0.98 1.05 1.08 1.26