Question

a) [2 points.] Suppose you have a project that has a 70 per cent chance of doubling and a 30 per cent chance of halving your investment in a day. (This is a high-risk project indeed.) i. Compute the expected return and volatility of a one-period investment. ii. Compute the expected return per day, given that you can renew the project each day for a very long period of time in principle infinitely). b) If a security lies above the SML, it is overvalued. True or false? The presence of risk means that i) investors may profit more than they expected, ii) more than one outcome is possible, iii) final wealth may be greater or lower than initial wealth. Which one(s) is/are correct? Explain shortly.

Answer 1

a). Expected Return of a one period investment.

Given: 0.70 chance of doubling and 0.30 chance of halving the investment in a day .

So, Expected Return: 0.70*2+ 0.30*1/2 = 1.55%

volatility of one period investment:

Probability	x	x-1.55	(x-1.55)2	Probability*(x-1.55)2
0.70	2	0.45	0.2025	0.14175
0.30	0.5	-1.05	1.1025	0.33075
			Sum:	0.4725

Volatility= (0.4725)1/2= 0.6874%

b) The statement is FALSE that the security lies above SML is overvalued.

Because all the correctly priced securities are plotted on SML line and those which are above the SML line, are the undervalued securities not overvalued. because for given amount of risk, they yield a higher return. whereas the securities below the line are overvalued as they provide lower return on a given amount of risk.

c) The presence od risk means:

ii) More than one outcome is possible. because risk is the possibility of something bad may happen. It involves uncertainty. So presence of risk indicates that more than one outcome is possible.