Tutorial week 1 Flashcards
Consider a one-year investment in two assets: the Vanguard S&P500 index (VFINX) and the Vanguard Short Term Bond mutual fund (VBISX). Suppose you buy one share of the S&P 500 fund and one share of the bond fund at the end of September, 2016 for $104.61 and $9.70, and then sell these shares at the end of September, 2017 for $97.45 and $10.46, respectively.
a) What are the simple annual returns for the two investments?
b) What are the continuously compounded annual returns for the two investments?
c) Assume you get the same annual returns from part (a) every year for the next 10 years. How much will $10,000 invested in each fund be worth after 10 years?
Why must it be the case that an investor with diminishing marginal utility of wealth is risk-averse?
A risk averse investor is defined as someone who will refuse a fair game (where the expected return is zero). They will do this because the utility associated with the loss of £1 is greater than the utility associated with the gain of £1. This is the same as saying the investor has a diminishing marginal utility of wealth. This leads to an upward sloping, concave trace in utility-wealth space.
How would you describe, using maths, an investor who prefers more wealth to less?
How would you describe, using maths
a) an investor who happens to be a risk lover?
b) an investor who happens to be risk averse?
c) an investor who happens to be risk neutral?
Consider a utility function of the form U(W)=lnW. Is this utility function consistent with risk aversion and non-satiation (prefer more to less)?
Suppose that your wealth is $250,000. You buy a $200,000 house and invest the remainder in a risk-free asset paying an annual interest rate of 6%. There is a probability of 0.001 that your house will burn to the ground and its value will be reduced to zero. With a log utility of end of-year wealth, how much would you be willing to pay for insurance (at the beginning of the year)? (assume that if the house does not burn down, it’s end of-year value still will be $200,000).
Using the assumptions of Exercise 4 and also assuming that the cost of insuring your house is $1 per $1,000 of value, what will be the certainty equivalent of your end-of-year wealth if you ensure your house at:
a)1/2 its value?
b) Its full value?
c) 1 and ½ times its value?
a) What is Homer’s expected value of the trip (assume no other costs incurred)?
b) What is Homer’s expected utility of the trip (use the above info only)?
c) What is Homer’s preferences relative to risk?
d) What is Homer’s ARA and RRA measures?
e) Is Homer increasing, decreasing or constant relative (absolute) risk averse?
