R31 (Return Concepts and Equity Risk Premium)

CFAI end of chapter Q8. I got it wrong and even rereading the solution lots of times I don’t get it so any additional insight is most welcome.

Equity risk prem is the prem for holding risky assets necessary to incentivise investors from the risk free asset. Q8 asks about the effect of the inclusion of data from a volatile period on the equity risk premium.

If the return on the index with including the volatile period is (say) 8% and the risk free return is 3% then the equity risk prem is 5%. If the period of instability was not included in the index the return would be higher (say 9%) but then the equity risk prem is 6%. As such does the inclusion of ths date not increase the ERP rather than decrease it as in the CFAI solutions?

are you making an implicit assumption somewhere that more volatile = lower returns? Volatility refers to the standard deviation of returns. So the mean return - and this is more often than not - would be higher than if the higher volatility period returns are not included.

so if that be the case - more volatile = higher returns - so mean return with inclusion is higher - when that higher period of unstable returns is removed - the mean return would be lower - leading all in all to - lower ERP.

Thanks CP, really appreciate the insight

Still got a question on it though.

The vignette stated that:

“Over 2004 to 2006 a series of military confrontations concerning a disputed border disrupted the economy and financial markets. The dispute is conclusively arbitrated at the end of 2006.”

I interpreted this as (temorarily) decresing returns and the solution in the text actually states that

“The events of 2004 to 2006 depressed share returns but 1) are not a persistent feature of the stock market environment, 2) were not offset by other positive events within the historical record, and 3) have led to relatively low valuation levels, which are expected to rebound.” I opted for A but B below is correct: “The events of 2004 to 2006 would be expected to: A) bias the historical equity risk premium estimate upwards. B) bias the historical equity risk premium estimate downwards. C) have no effect on the historical equity risk premium estimate.”

since the issue was resolved at the end of 2006 - the returns after the dispute was resolved would be higher. now if you go and include the returns during the period - the returns would be biased downwards.

Think I kinda got it CP - thanks smiley

Gallagmp: I think your initial example was correct

during the period of instability the prices would drop. However now, the issue has been resolved. So now the prices have increased. Inclusion of period of instability would lower the returns and hence lower the ERP. I think this is what the question is getting at.

and they are asking about the Historical equity Risk premium. IF the period of instability had NOT been present the historical Equity risk premium would have been higher. Including the period would cause the historical equity risk premium to be now lower.

I agree totally, I’m just saying that OP’s example actually says that (i.e. including period of instability lowers ERP).

his example may have stated that - but his final conclusion actually did not.

Right, so just pointing out he had it right and ended up confusing himself!

sorry to re-open this topic:

The vignette stated that:

“Over 2004 to 2006 a series of military confrontations concerning a disputed border disrupted the economy and financial markets. The dispute is conclusively arbitrated at the end of 2006.”

I interpreted this as (temorarily) decresing returns and the solution in the text actually states that

“The events of 2004 to 2006 depressed share returns but 1) are not a persistent feature of the stock market environment, 2) were not offset by other positive events within the historical record, and 3) have led to relatively low valuation levels, which are expected to rebound.” I opted for A but B below is correct:

“The events of 2004 to 2006 would be expected to: A) bias the historical equity risk premium estimate upwards. B) bias the historical equity risk premium estimate downwards. C) have no effect on the historical equity risk premium estimate.”

my qn is why wouldn’t the period of instability btw 2004 to 2006 raise the risk premium since investors should rightfully be required to earn more as a result of holding stocks that are more risky

That’s my question as well! I would think that the equity risk premium would increase during volatile times (i.e the period 2004-2006) to compensate investors for taking on risky investments…

I am having the same issue with this question. This topic is now under Reading 25.

The conflict over 2004-2006 reduced returns, and correspondingly would have increased the equity risk premium (ERP) over the period. Including this period would logically bias the ERP upwards.

The solution isn’t convincing. On (1), why would you need an effect to be persistent to affect ERP? A conflict would logically raise ERP. Its extremely frustrating going through this problem set.

The prior question (Qn 7) is also problematic as it does state whether we should factor in the 2004-2006 conflict, which was stated in the problem set.

The question reads: "The inclusion of index returns prior to 2001 would be expected to:

A) bias the historical equity risk premium estimate upwards.
B) bias the historical equity risk premium estimate downwards.
C) have no effect on the historical equity risk premium estimate.”

The solution states (A) as the right answer due to survivorship bias.

Assuming the period prior to 2001 was a relatively stable period vis-a-vis 2004-2006, ERP would have been lower (due to stable/better performing markets) and including that period would bias the ERP downwards.

I also had trouble with this one.

The definition of ERP “is the incremental return (premium) that investors require for holding equities rather than a risk-free asset.” An investor would require a HIGHER ERP in 2006, looking to invest during the start-middle of the conflict because of higher risk.

But the book states:
“Possibly confusingly, equity risk premium is also commonly used to refer to the realized excess return of stocks over a risk-free asset over a given past time period.” This is what this question is telling us. We have to assume that the realized “excess of return” during these conflict years was LOWER. ("confrontations concerning a disputed border disrupted the economy and financial markets.”)

This seems to be a paradox. Before investing ERP is higher, but after the years you notice ERP was actually lower than average.