Question

Which of the following indexes requires frequent rebalancing?

[I] Value-weighted index
[II] Price-weighted index
[III] Equally-weighted

		I only
		II only
		III only
		II and III only
		I, II and III

An investor invests 60% of her wealth in the market portfolio with an expected rate of return of 12% and a variance of 0.01, and she puts the rest in Treasury bills that pay 2% per year. What is the standard deviation of the portfolio?

		4%
		6%
		7.5%
		10%
		None of the above

You are an investment advisor for Alan and Jimmy. You've helped them optimally allocate their investment portfolios along the same capital allocation line (CAL). If Alan's portfolio has a higher weight on risk-free asset than Jimmy's portfolio, then which of the following statements MUST be true:

[I]   Alan’s portfolio has lower expected returns than Jimmy’s
[II]  Alan is less risk-averse than Jimmy
[III] Alan must hold a positive position in the risky asset

		I only
		I and II
		I and III
		II and III
		I, II, and III

The table presents forecasts of the returns of stock market and probability of each state of the economy for next year. Calculate the expected return.

State of Economy		Return	Prob. of State
Recession		-12%	0.15
Normal		6%	0.60
Expansion		20%	0.25
			4.7%
			6.8%
			8.4%
			10.4%
			None of the above

On Jan 1, you sold short 400 shares of AT&T at $35 per share. You post $7000 to the margin account. On April 1, you received a margin call on this trade. Assume the minimum margin requirement is 40%, what is the price of the stock that triggered the margin call?

		$29.17
		$37.5
		$39.25
		$43.75
		None of the above

Answer 1

I have answered first and second questions. Please get back to me in case of any clarifications. Hope this helps!

1)

answer) Equally weighted

As securities market is so dynamic, the prices of constituent stocks vary continuously. As prices varies, to maintain the equal weights, frequent re balancing is necessary.As each re balancing activity associated with some transaction cost, the overall transaction cost will also be high for equally weighted

2)

answer) 6%

weight in market portfolio = 60%

weight in t bills = 40%

expected return in market portfolio = 12%

variance of market portfolio = 0.01 given

standard deviation of market portfolio = square root(0.01) = 0.1 = 10%

expected return in t bills = 2%

since standard deviation of risk free asset(T-Bill) is zero, the standard deviation of portfolio will be equal to standard deviation of the market portfolio multiplied by its weight

so, the standard deviation of the portfolio = 60% * (10%) = 0.06 = 6%