When calculating Jensens alpha, do you use the expected market return, or the actual market return for a specific period?
In (Jensen, 1968, p. 391) Jensen writes:
“We now wish to show how (1) can be adapted and extended to provide an estimate of the forecasting ability of any portfolio manager. Note that (1) is stated in terms of the expected returns on any security or portfolio j and the expected returns on the market portfolio. Since these expectations are strictly unobservable we wish to show how (1) can be recast in terms of the objectively measurable realizations of returns on any portfolio j and the market portfolio M.”
Does this mean that you should use the actual return for the market and not the expected return? Yet, I read everywhere that you use the expected market returns.
Pretty sure its the ER of the market and the beta of the security. Anything in excess of the CAPM expected return is alpha… be sure to multiple the beta by the MRP and not just the absolute return
If you’re doing an attribution (i.e. how much alpha did we generate), you use the actual market returns.
If you’re doing a projection (how much return do we think this will produce going forward), you use expected market returns.
So your asset has a beta of 1.2, it delivered 15%, the market delivered 11% but was expected to deliver 8%. Treasurys are yielding 1%.
Market excess return (11% - 1%) = 10%.
Your asset should have delivered 1.2*10% + 1% = 12% + 1% = 13% based on its Beta and RFR. But instead it delivered 15%, so the Jensen Alpha is 2% (= 15% - 13%). (13% is the EXPECTED return ON THE ASSET, given what the market actualy did. Alpha is the difference between the expected return on the asset given what the market actually did and the actual return on the asset. There’s an ASSET expected return based on the market’s actual return, but there’s no place for the expected market return in this calculation, so maybe that’s where the confusion lies).
Going forward, if you expect the market to deliver 8%, then 7% (=8% - 1%) is the market’s excess return. You expect the asset’s returns from beta to be 1.2*7% + 1% = 8.4% + 1% = 9.4%. If you think you’ll get the same alpha of 2%, that means that you expect 9.4% +2% or 11.4% going forward.
More often, you’ll try to come up with an expected return on the asset based on your fundamental analysis and financial statements, then compare that return with what you’d expect from a pricing model like CAPM or APT (or sometimes just a fixed hurdle rate). Alpha is the difference between those two figures. That’s actually what Equity Research people are doing when they discount cash flows using an asset pricing model’s discount rate, but they often don’t have a good enough view of the big picture to realize that that’s actually what they are doing: if those cash flows generate a return higher than what the pricing model says it should deliver, you’ll wind up with an asset that looks underpriced, and vice versa for overpriced.