FIN $604$: Global Financial Markets and Institutions

Problem Set: Lesson $2$

Suppose there are $n$ uncorrelated assets in the market. You, a mean$-$variance optimizing

investor, may invest in one or any combination of these risky financial assets over the next

period. The expected rate of return $$ is the same for each asset. However, the riskiness of

the assets are different such that ${}_1<msub\; id="EditorElement\_343651"><mrow><mi\; id="EditorElement\_343644"></mi></mrow><mrow\; id="EditorElement\_343650"><mn\; id="EditorElement\_343647">2</mn></mrow></msub>$dotsdots

a$)$ Show the assets on a mean return$-$standard deviation graph.

b$)$ Describe the feasible and efficient sets of investments and visually show rough

representations on the graph you drew for part a$.$

c$)$ Can a rational and risk averse investor such as yourself form a portfolio through

diversification that is better than each individual asset? Explain.

Consider three mutual funds. The first is a stock fund, the second is a long$-$term

government and corporate bond fund, and the third is a Treasury$-$bill money market fund

that yields a rate of $8\%.$ The probability distribution of the risky funds is as follows:

The correlation between the risky fund returns is $0\mathrm{.}3.$

$($a$)$ What are the investment proportions in the global minimum$-$variance portfolio of the

two risky funds? Find the minimum by setting the first derivative of the variance with

respect to the weight of one asset equal to zero. What's the expected value and standard

deviation of the portfolio?

$($b$)$ Tabulate and draw the investment opportunity set of the two risky funds. Use

investment proportions for the stock of zero to $100\%$ in increments of $20\%.$

What is the justification for exploring conditional CAPM models? Consider conditional

CAPM model of Jagannathan and Wang $($JoF$,1996).$ How do they reach an unconditional

multi$-$factor model and what are their factors? How do they address one of the main points

of contention in classical asset pricing models, namely proxy for market portfolio? Explain

their reasoning? What is the measure they use? How do their results improve upon the

static CAPM model?