Serving the Quantitative Finance Community

lwb120
Topic Author
Posts: 3
Joined: July 30th, 2004, 7:59 pm

### CAPM question

CAPM: ri=rf+b(rm-rf)in general, we are given the return on S&P 500 index, say 12%, as rm in the fomula, but how can we work out this number? if we use the S&P data on yahoo finance, and then calculate return through r=ln[p(t)/p(t-1)], the return shall be negative sometimes.

JamesH83
Posts: 817
Joined: June 25th, 2003, 11:38 pm

### CAPM question

sure it will be negative sometimes.calculate the average annual return over a long period and you will get something that looks about right.

lwb120
Topic Author
Posts: 3
Joined: July 30th, 2004, 7:59 pm

### CAPM question

if rm is negative, then ri is negative, why not turn to invest risk free maket? in this case, is CAPM still valid?

GregWallace
Posts: 157
Joined: August 6th, 2004, 3:31 am
Location: United Kingdom
Contact:

### CAPM question

Hi lwb 120As James H83 mentioned CAPM is more of a long-term or strategic measure.You are right that if ri is negative then DON'T invest in the underlying security (or short it if you are able).Thus CAPM is giving you exactly the correct signal.There is however, another issue.Please do not confuse historical estimates as predictions of the future.The measures you use in CAPM (or any single-factor or multi-factor model) need to be consistent.A measure in the past is a measure in the past.Any action you are taking is an action in the present for a return in the future.Yes, there are ways of using historical data in a sensible way to assist you forecast future measures.And there are copious examples of people using historical data blindly and in a very poor way to give almost no insight as to future measures.And the unfortunate thing is that they do not even recognise they are doing it.So when you reflect, what do you discover?

snowdew
Posts: 78
Joined: June 3rd, 2004, 4:27 pm

### CAPM question

as others have pointed,the returns and betas should be negative sometimes during your examined period.However CAPM is a single factor model,thus averaging over several years wouldn't give good indication either,realistically regular return should look like a zigzag line with different r's and b's in each period.For this characteristics it is only good when considering long term effect,say 10 years or more.on the other hand you might have got negative returns from irrelevent daily/weekly volatilities,is your historical data per month or per day ?

DavidJN
Posts: 1781
Joined: July 14th, 2002, 3:00 am

### CAPM question

The short answer to the original question is that the CAPM is an ex ante model - i.e. it relates the expected return to systematic risk. It is more properly written as E[Ri]=Rf+B(E[Rm]-Rf). We expect returns (including E[Rm]) to be positive, but ex post they may not be. The model is of limited usefulness because it expressses the unobservable expected return E[Ri] in terms of another unobservable, E[Rm]. That is to say, it is not reduced form. Further, there is no practical proxy for E[Rm] because, in theory, it contains all risk assets, not just financial.

stephan

### CAPM question

Hi there,DavidJN is perfectly right - expected return is positive in CAPM by assumption; the key is market risk premium, which can be negative "ex post" and should (must!?) be modelled via dummy-variables. This could be of interest for you:http://www.wiwi.uni-frankfurt.de/schwer ... .pdfCheers, Stephan

Benjamin1977
Posts: 20
Joined: July 21st, 2010, 9:43 am

### CAPM question

Dear All,A simple, and naive question: why would the CAPM model be market capitalized? Where wuld market cap be taken into account in computations?Many thanks

prfj
Posts: 19
Joined: December 11th, 2011, 10:36 am

### CAPM question

Benj: the market portfolio is the efficient portfolio, the efficient portfolio is a portfolio of all possible investments. weighted by market cap.
Last edited by prfj on December 28th, 2011, 11:00 pm, edited 1 time in total.