Arithmetic and geometric risk premiums

Mballack · February 21st, 2011, 8:21 pm

I had always the impression is that the arithmetic risk premium is nothing but the sum of risk premiums over the years divided by the number of years. I was reading Mckinsey (look at the attachment) and I have no clue about the meaning of their formulas. They don't make sense to me.why 1+arithmetic average is the sum of (1+rm)/(1+rf) ? it is very confusing. Any help is appreciated.

acastaldo · February 21st, 2011, 10:30 pm

It is a matter of slightly different definition of "premium"You think the ex-post risk premium in a given year is rm-rfthey think it is prem = -1+(1+rm)/(1+rf) = (rm-rf)/(1+rf)(a similar confusion arises in computing inflation adjusted interest rates: do you just subtract the inflation or do you use a formula like the second one. I believe the second one is preferable theoretically [it shows how 1+rf and 1+prem compound together to give 1+rm i.e. (1+rf)(1+prem)=(1+rm)], the first is more convenient and easier to do in your head).