# SML with negative returns

I just wanted to quickly plot a SML in Excel and was bewildered to find that it sloped down, given my parameters were the NYSE over the past 12 months as market and a random tech stock. Both market and stock have negative returns over that period. I found that in Jansen’s 1972 article on CAPM a negative SML is mentioned. But I struggle withe the interpretation. Is a negative SML possible and explained by CAPM? If yes, the interpretation would reverse, right? Is there a good, acknowledged, way to transform a downward sloping SML into an upward slowing one without breaking the usual CAPM interpretation? Any suggestions and pointers are greatly appreciated. Edit: I tried absolute value and alpha for E® already but I am unsure about their appropriateness…

It sounds like you have negative betas

The betas are positive but the term (Rm-RFR) is negative because the expected market return, based in historic stock price over the period not considering dividends, is negative. Feel free to correct me: http://spreadsheets.google.com/ccc?key=pqBoKKhLO10_kW336XvZIWw

Bump, nobody having any thoughts on downward sloping SML?

Do you really believe that the last 12 months of returns would produce the best estimate of future returns?

No, I don’t believe historic returns necessarily provide the best estimate of future returns. I am also aware that if one would believe that future returns for an asset will be negative, going short on that asset would again result in positive returns. I am interested in using SML strictly to classify an asset as either over or undervalued. After several discussion I believe that an absolute value transformation of the term beta*(expected market return - risk free) is suitable for any downward sloping SML used to visualize over or undervalued assets.

I think it is a sample size problem. The theory behind the CAPM, SML uses unknow populations and uses sample parameters to estimate them based on observations. If your observations are very narrow, you cant get an accurate estimate of the unknown population. The true nature of pricing is unknown, we can only hope to use most efficient estimators. If it was known, then everyone who knew how the population actually worked would be billionaires and never share the formula.

The slope of the SML is the MRP. So that means that, in your graph, the MRP is probably negative. So, under what circumstances can the MRP be negative? That is, Rm-Rf<0? Only if Rf>Rm. As at today, the markets’ trailing-twelve-months returns are below that of the risk free rate, and they’re all negative. Right now, investors are not compensated even for systematic risk.

Right JS. Put into the large sample size, this would have a small impact on the overall historical measurement, but taken as a small sample, it is useless information.