# M Squared Measure

Page 166 of Reading 41 (Book 6) interprets M Squared as an “incremental return over a market index of a hypothetical portfolio blah blah blah”

Then in the same paragraph it says m-squared measures what the account 2would have returned if it had taken on the same total risk as the market index.

I know M squared measures the return earned on account assuming it takes on the same level of risk as the market portfolio … to me M squared is the total return earned on the portfolio compared with the market portfolio return at the same level of standard deviation. I don’t think M squared is the incremental return; it’s the total return, the incremental return would be M squared minus Market Portfolio return - any thoughts?

M2 = Rf + Portfolio Sharpe X market standard deviation

Therefore M2 = Rf + Scaled Portfolio Excess Return at market standard deviation -> M2 is a total return measure not an incremental return.

Going_For I dont think it is meant to be incremental total return in which case yo uare right but incremental return per unit of market risk

Here is my understanding of the formula:

M2 = Rf + Portf Sharpe x market st dev

or

M2 = Rf + (Rp - Rf) x (market st dev/port st dev).

In order to compare apples to apples, M2 is converting the incremental portfolio returns such that it now acts like a market index (with market deviations). So M2 is a measure of an incremental return (Rp - Rf) in Market risk units over the market return. While sharpe measures an incremental return per unit of portfolio st dev, M2 measures an incremental return that has market volatility. So it’s not really a total return measure.

To illustrate it.

Rf = 5%,

Rp = 8%

MarketStDev = .3

PortStDev = 1.2

M2 = 5% + (3%) * (0.3/1.2) = 5% + 0.75%.

So M2 says that the portfolio earned an incremental return of 0.75% over market index return of 5%.

M2 of market portfolio is its return

To compare M2 of 2 portfolios,just look at the Sharpe ratio of the two because other items in the M2 formula are constant - Rf and sigma (m)

You sure?

Rf = 5% is the risk free rate. So that incremental return of 0.75% is the return earned over the risk-free rate, not the market index return. M2 would measure incremental return over Rf but not over the market portfolio the account is being compared with.

I think the best way to go about it is consider M2 a total return measure at the same level of risk as market portfolio. Compare that total return with the market portfolio return, if the account’s M2 return measure is better than the market portfolio, then the manager added value.

You are right. Rf is the risk free rate, not market index return.

Let me rewrite the formula and correct myself.

M2 = Rf + (Rp - Rm) x (mkt stDev/ Ptf stDev)

So the 0.75% is an incremental return over market index of Rm at the market risk. And I also agree with your last paragraph. If you are just looking at M2 given the two managers earned the same return and one had a higher StDev than the other, the manager with a higher M2 would be evaluated as being better at making incr return over its market index at a lower StDev.