Lymann Brothers Has a Substantial Number of Clients Who Wish

question 54

Essay

Lymann Brothers has a substantial number of clients who wish to own a mutual fund portfolio that closely matches the performance of the S&P 500 stock index.A manager at Lymann Brothers has selected five mutual funds that will be considered for inclusion in the portfolio.The manager must decide what percentage of the portfolio should be invested in each mutual fund. $$\begin{array}{l}\text { Annual Returns (Planning Scenarios) }\\\begin{array} { l r r r r } \text { Mutual Fund } & \text { Year 1 } & \text { Year 2 } & \text { Year3 } & \text { Year 4 } \\\hline \text { International Stock } & 25.64 & 27.62 & 5.80 & - 3.13 \\\text { Large-Cap Blend } & 15.31 & 18.77 & 11.06 & 4.75 \\\text { Mid-Cap Blend } & 18.74 & 18.43 & 6.28 & - 1.04 \\\text { Small-Cap Blend } & 14.19 & 12.37 & - 1.92 & 7.32 \\\text { Intermediate Bond } & 7.88 & 9.45 & 10.56 & 3.31 \\\hline \text { S\&P 500 } & 13.00 & 12.00 & 7.00 & 2.00\end{array}\end{array}$$ Minimize the variance of the portfolio subject to constraints on the expected return,assuming that Lymann Brothers' client requires the expected portfolio return to be at least 9 percent.

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Definitions:

Two-Factor Theory

A theory of emotion developed by Schachter and Singer proposing that emotions are determined by both physiological arousal and cognitive labeling of the cause of that arousal.

Spillover Effect

The phenomenon where an event or behavior in one domain or area influences another, often used in economics, psychology, and environmental science.

Cannon-Bard Theory

A theory of emotion that suggests that emotional experiences occur simultaneously with physiological responses, rather than one causing the other.

Cannon-Bard Theory

A theory of emotion that proposes emotions and bodily responses occur simultaneously, rather than one causing the other.