CAPM and Risk Load

[volleyball]

I'm finding the risk load calc using CAPM a little confusing. Specifically question 11d(99-9-37).
The formula Rf+B(Rp-Rf) is equal to what? (Return on ?)
I think there is some inconsistency in the notation used in the answer as the formula above is substituted in the risk load equation as Rp (which of course is in the middle of that formula)

But there's some discussion of converting this ROE to Return on Premium using leverage ratio, Rm=Rf+ (P/zSB)Rp

I'm a little confused on which formula to use and when given the info in that question and the confusion notation in the answer doesn't help.

From the looks of the recent posting I'm a little behind everyone as I have yet to start the experience rating section. Hopefully someone can help in the earlier papers.

Please help clarify!!! :burn:

[Colymbosathon ecplecticos]

The CAPM formula you gave is for the expected return of a portfolio with a given beta (which you called B).

The Rp in your formula should be the expected return on the market.

[volleyball]

I agree however the solution given says the formula is Rp (even though Rp is in the formula given as the solution). Do they mean the expected return on the portfolio not "Return on Premium"?
I think the notation is confusion me. What would your formula be for the resulting risk load?

Thanks :bighug:

[Colymbosathon ecplecticos]

Hard to answer without seeing what you are looking at.

Maybe others can help with this one.

[volleyball]

Is there anyone out there that understands the application of CAPM to risk loads as mentioned above?
Anyone?
Anyone?

[Pack Fan]

The simple answer is that this section is not on the syllabus anymore. Only the Bault review is on the exam, which only comments on the method.

Bault questions Feldblums method of converting CAPM return to a profit load using (P/zS). Bault states that the most CAPM can accomplish is to compute profit load relativies, because the leverage ratio impacts the profit load for every individual line of business.

[volleyball]

Thanks for the sum up, still that question is going to bother me till I write because I don't understand clearly their line of thinking. And if it shows up on the exam .....

Thanks, here's to hoping that question doesn't reappear.

[Utopial]

I'm not clear on this topic either. I was a bit confused by the notation and the discusion of particular terms in each formula

CAPM:
Re = Rf + B(Rm - Rf)
where u vary the rate of return (Re? or Rm?) but keep leverage stable for each LOB

Leverage Ratio Approach:
Rm = Rf + Rp * P/zSB
where u vary the leverage but keep rate of return (Rm) stable for each LOB

my understanding is that:
Rm = target return on equity for risk x
Rp = return on prem
Re = return on equity for the industry portfolio
Rm = return on market portfolio
P/zSB = prem to surplus leverage ratio for x

How do these formulae relate to one another?

[carrytheCrøss]

Very ironic that you bump this thread today since I was having difficulty trying to piece together Bault's paper and found this same thread yesterday.

Leverage Ratio Approach:
Rm = Rf + Rp * P/zSB
where u vary the leverage but keep rate of return (Rm) stable for each LOB

CAPM:
Re = Rf + B(Rm - Rf)
where u vary the rate of return (Re? or Rm?) but keep leverage stable for each LOB

I agree with what you've written here, but simply for reading ease, I'll restate them as
\text{Leverage Ratio Approach: }R_m = R_f + R_p * \frac{P}{zS\beta}
\text{CAPM: }R_e = R_f + \beta(R_m - R_f)

How do these formulae relate to one another?The leverage ratio appraoch implies that R_m-R_f=R_p * \frac{P}{zS\beta

Substituting this result into the CAPM approach, we get R_e = R_f + \beta(R_m - R_f)=R_f + \beta*R_p * \frac{P}{zS\beta}=R_f + R_p * \frac{P}{zS}

I believe this last CAPM equation suggests that the return on equity for the industry portfolio is simply "the risk-free rate + return on premium * industry leverage ratio".
The leverage ratio equation suggests that the return on equity for a single risk x's portfolio is "the risk-free rate + return on premium * industry leverage ratio adjusted for risk x".

Thus, if all the variables mean the same thing in each equation, I believe these equations are directly analagous. Maybe someone else can clarify/add something, but I hope that helps.

[Utopial]

thanks

When they say that for CAPM u vary the rate but keep the leverage stable, is the rate being referred to Re?

And for the leverage ratio approach u vary the leverage but keep the rate stable is the rate Rm?

[carrytheCrøss]

And for the leverage ratio approach u vary the leverage but keep the rate stable is the rate Rm?Yes.

When they say that for CAPM u vary the rate but keep the leverage stable, is the rate being referred to Re?Not sure. I believe that if we accept a single leverage ratio, then we must demand different rates of return on equity based upon the line's beta.

I feel like I may have screwed something up in my explanation above . . . I think it has to do with the R_e term since I'm not quite sure whether this is, in fact, the return on equity for the industry portfolio.

Sorry for the late reply.

[Examinator]

Do we have any confirmation that Re really is the industry ROE? I thought I understood this but the more I look at it the less cohesive it becomes. I also follow Cross's explanation, but the target Rm for x and the Rm in the CAPM is throwing me too.

[Examinator]

The answer to this may be on page 85.

If you accept a single leverage ratio (i.e., P/{Sz}), then you must demand differing rates of return on equity based on the line's β (it seems like this has to refer to Re, which would differ depending on the line of business).

But if you adjust the surplus requirements by β (i.e., the leverage ratio becomes P/{Szβ}), then you can accept an equal rate of return on equity (Rm) across all lines, and this will equal the industry rate (tying in that Rm in the leverage ratio approach equals Rm in the CAPM approach).

So, Cross's explanation is right on, and Re is the ROE for an individual line of business when using a common surplus requirement.

Maybe? :-?

[carrytheCrøss]

But if you adjust the surplus requirements by β (i.e., the leverage ratio becomes P/{Szβ}), then you can accept an equal rate of return on equity (Rm) across all lines, and this will equal the industry rate (tying in that Rm in the leverage ratio approach equals Rm in the CAPM approach).I think that makes sense. Thanks for looking into this.

[Utopial]

ok so basically:
- Betas always vary by LOB
- CAPM: varying Beta + stable P/zS (leverage) = varying Re
- Leverage Approach: varying Beta + counter-varying P/zS = stable Rm

if Rm is the same in each of these (ie the stable market rate), shouldnt Rp = Re - Rf = 'premium' ie 'excess' return for a particular LOB?

i guess the main thing is knowing wat is stable and wat is varying in each situation. they seem to be the same formula but CAPM nullifies the leverage impact by effectively setting P/zS to 1 and the leverage formula uses the simplifying notation Rp instead of 'Re - Rf'

[Examinator]

ok so basically:
- Betas always vary by LOB
- CAPM: varying Beta + stable P/zS (leverage) = varying Re
- Leverage Approach: varying Beta + counter-varying P/zS = stable Rm

The way I understand it is that with the CAPM, β varies by LOB, and together with a constant leverage ratio results in an Re that varies by LOB.

With the leverage approach, the leverage ratio varies with β, giving a constant Rm for all lines of business (which would otherwise vary if it weren't for the varying β). I think this is what you're saying, but I'm restating it for my sake, if nothing else.

if Rm is the same in each of these (ie the stable market rate), shouldnt Rp = Re - Rf = 'premium' ie 'excess' return for a particular LOB?This isn't clear to me.

i guess the main thing is knowing wat is stable and wat is varying in each situation. they seem to be the same formula but CAPM nullifies the leverage impact by effectively setting P/zS to 1 and the leverage formula uses the simplifying notation Rp instead of 'Re - Rf'I agree that this is probably the main concept to take from this part of the paper.