# 3 questions - ERP, asset allocation, Monte carlo

1. Please remove my doubts regarding market risk premium and equity risk premium once and for all. I still get confused even in level 3 (no hope !! ) Ri = Rf + beta * (Rm - Rf) I thought (Rm - Rf) = market risk premium beta * (Rm - Rf) = Equity risk premium Just saw a sample exam where (Rm - Rf) is referred to as equity risk premium. can that be right? 2. Is “investor risk tolerance is constant” for both Strategic asset allocation and Tactical asset allocation? I have seen statements where either one of the asset allocations are being discussed and statements appear like “investor risk tolerance is constant” 3. CFAI Vol 5 page 279, Problem 12. It is a monte carlo var problem. They are asking to calculate 5% annual var. we are provided with 40 worst returns of 700 outcomes. we are also provided with expected return and standard deviation. I thought Monte Carlo method uses the same formula as variance covariance method. However CFAI solves it using similar method as Historical method. ??? Thanks in advance for help.
1. I agree, market risk premium is (Rm - Rf). But, I don’t the CFA defines ERP as beta * (Rm - Rf)? I say that because this is the expected rate of return. Whereas, I thought ERP is linked to the required return. 2) It makes sense that it would be for “Strategic”, because you’re rebalancing to prescribed weights. I think it is for “Tactical”, even though you’re shifting weights of the risky assets based on short-term expectations… because the analytical framework doesn’t address a change to risk tolerance (which would change the tactical behavior). However, not sure if the readings say? 3) You would do a similar exercise as with historical VAR because it’s just a statistical exercise. They have the 40 worst outcomes out of 700, so pick the 35th worst as 5% VAR. The format’s confusing, but they only have so many ways to test Monte Carlo simulation (with a non-statistical crowd anyway).

drymartini Wrote: ------------------------------------------------------- > 1. Please remove my doubts regarding market risk > premium and equity risk premium once and for all. > I still get confused even in level 3 (no hope !! > ) > > Ri = Rf + beta * (Rm - Rf) > > I thought (Rm - Rf) = market risk premium > beta * (Rm - Rf) = Equity risk premium Equity risk premium is typically not defined for a specific stock but rather for an index. If your Rm is based on a stock index (such as SP500), that Rm-Rf would be equity premium as well as market premium. > 2. Is “investor risk tolerance is constant” for > both Strategic asset allocation and Tactical asset > allocation? constant risk tolerance is an assumption that should be specified in the question. I wouldn’t assume constant risk tolerance (constant risk aversion) if it’s not given. Markowtiz model though assumes constant risk tolerance. > 3. CFAI Vol 5 page 279, Problem 12. > > It is a monte carlo var problem. They are asking > to calculate 5% annual var. > we are provided with 40 worst returns of 700 > outcomes. > we are also provided with expected return and > standard deviation. > > I thought Monte Carlo method uses the same formula > as variance covariance method. However CFAI solves > it using similar method as Historical method. both methods are fine. those calculating quantiles is more accurate than estimating VaR using standard deviation as that implies normal distribution.

OK, I will weigh in. drymartini, you are correct, the CAPM provides a means of estimating the equity risk premium for a spefic stock. It’s as you define it. Equity Risk Premium = beta*Market Risk Premium. if you saw this: “Just saw a sample exam where (Rm - Rf) is referred to as equity risk premium. can that be right?” It is not correct. Rm - Rf is the market risk premium. 3. Monte Carlo VaR - correct, you are not imposing distributional assumptions on the process. So you just choose the worst 5% case, if this is what your confidence level is, as described by NeverUse … the difference is in variance-covariance method, you are implicitly assuming normal distribution (let’s say) so you can just use r - 1.65 standard deviation etc.