Utility and Expected Return question

CFA Level I
#1

I came across this question and I got stumped:

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Thanks!

#2

Variance and return expectation do not change between investors based on subjective measures (like risk aversion) if it is the same security or portfolio of securities. Utility can also be defined as preference and does change between each individual… so it has to be A, formula aside.

#3

Ok, that makes sense, could you give an example of what would change variance and return expectations? Just for my understanding. I’m guessing these are objective measures.

#4

Variance would change if an additional data point was added, n would increase and the numerator would also change provided the data point isnt exactly equal to the mean. Think of the formula for variance. Return can be calculated through CAPM, DCF and DDM and would change because variance changed (effecting beta in CAPM and required return in DDM). IF we both went to a casino and I had a net worth of $100 and you had a net worth of $1,000,000 we could both go put $50 on roulette, on red. I would be much more risk averse and gain much more utility from the bet if it hit because I am risking half of everything. You on the other hand would be willing to risk much more (less risk averse) and would not gain as much utility if the $50 bet hit. The variance and return is the same, the utility is not. Hopefully this helps and did not confuse you.

#5

Perfect casino example!!! Thanks! :slightly_smiling_face:

#6

Variance wouldn’t necessarily change from the addition of an additional observation. The variance is the EXPECTED squared deviation. If the new observation is drawn from the same distribution, its squared deviation should be the same as the average squared deviation of the rest of the distribution.

And if the observation were at the mean, it would clearly change the variance (unless it’s a degenerate distribution, like for a risk-free asset).

#7

One of the assumptions of Modern Portfolio Theory is homogeneous expectations: Bob and Mary always have the same expectation for the return, standard deviation of returns, and correlations of returns for all investments.

In the real world, of course, that’s silly. But that’s one of the underlying assumptions. When you agreed to play this game, you agreed to abide by its assumptions.