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portfolio theory

Thread starter #1
Hi David,

bugging u again.

here ane my doubts:

since all investors want to hold the same risky portfolio,risky portfolio m must be market portfolio..am unable to comprehend this line in core readings.why will investors want to hold same risky portfolio?

2.why variance of return of market portfolio is the return covariance of market portfolio with itself.

3.also in difference between CML and SML.we just pt the value of SD of portfolio in CML in covariance terms with market,it becomes CML.But for a portfolio unsystematic risk will already be removed.


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi Anil,

1. It is a very narrow conclusion that follows from unrealistic set of CAPM conditions. It is only because it assumes that all investors are "robots" with identical information, identical "mean variance" tendencies (risk aversion) and identical thought process. Really, it is like saying: every market participant is a robot with the same code - give each robot the same input, they come to the same conclusion; i.e., hold the market portfolio.

Why the market portfolio? B/c it is the ultimate diversification (all systemic risk, no idiosyncratic risk). If you are one of the robots, and you hold only domestic equities, you will want to add international to gain a diversification advantage, then you will want to add commodities, and on and on, until you hold the market. (Do you notice how studies of a new asset class will always "sell" their ability to diversify. It is like we buy into this for every asset class in the market. Theoretically, under these assumption, any asset class has some incremental diversification value). And, all of the other paricipants conduct the *same process* so you all end up holding the market. *But* note, the total portfolio on the CML = market (M) + risk free asset. So, while everyone holds (M), they may hold different proportions of (M) and riskfree

2. It follows from: COV(X,X) = VAR(X). Like a correlation of an asset with itself is 1.0, the covariance of an asset with itself is its variance. This formula is absolutely key:

Correlation = COV(X,Y)/[std dev(x)std dev(Y)]
COV(X,Y) = Correlation*[std dev(x)std dev(Y)]

Now plug in Y=X, and you have
COV(X,X) = Correlation (X,X)*[std dev(x)std dev(X)]
= (1) * Variance (X)

3. I think i see what you are saying...CML and SML are both return versus risk. CML is return versus risk of portfolio = market + riskfree asset [i.e., standard deviation of this portfolio that includes only the two components, the market and the RF asset, but held in different proportions]; SML is return versus risk of an *individual asset* where risk is beta of the asset instead of standard deviation precisely *because* assets on the line are presumed to have no idiosyncratic risk and only systemic risk (i.e., only systemic risk, so only need beta to measure their risk). For both, CML and SML, for points on the line, it is only systemic risk - idiosyncratic risk (alpha) signifies a point "off the line"...but again, i'd keep in mind they are similar in the sense they are both risk/return but the CML is a plot of "efficient" portfolios while SML plots assets (in the world where asset return is only a function of asset's systemic risk, beta)

Hope that helps, David
Thread starter #3
thanks David,

that was helpful.

one more doubt:

why is RAROC misleading (why we need adjusted VAR)? i was not able to get what the author was trying to say from core readings(keeping probability of default constant paragraph)


David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi Anil,

I just uploaded today the XLS that replicates this *difficult* idean in Crouhy (Table 14.4). You might or might not find it interesting...
The point is that "first generation" RAROC is flawed because it can be increased due to volatility and systemic correlation (i.e., a higher equity beta). In other words, you can increase RAROC and make a project more desirable by investing in a risky project.
So the 2nd generation RAROC incorporates/adjusts for the risk...