# What are the implication of a negative risk-free rate on SML?

What happens to the Security market line (within the CAPM model) when the risk-free rate turns negative?

-
First Comment: Are negative rates really consistent with the assumptions underlying CAPM? For example why would anyone invest risk-free instead of consuming wealth immediately? – g g Jul 10 '14 at 15:17
Second comment: Does CAPM still make any sense as a model if risk free rates are negative? One could hold cash in physical notes in a safe vault earning zero which means negative risk free rates create arbitrage opportunities. So the fact that negative risk free rates are possible at all can only be explained with features not contained in the CAPM model, such as the cost of safe bank vaults or the fact that there is no risk-free asset in the first place. – g g Jul 10 '14 at 15:18

The risk-free rate is the y-intercept of the Security market line. If the risk free rate goes negative the y-intercept of the Security market line would simply be below the x-axis. So if the risk-free rate decreases the whole line shifts down. This just means people are willing to pay for safety. According to the formula for the SML:

• E(Ri) : expected return of a security
• E(Rm) : expected return of the market
• B : systematic risk
• Rm : market risk
• Rf : risk-free rate

E(Ri) = Rf + B(E(Rm) - Rf)

-

When we discuss CAPM it assumes a lot of things about the market and investor behaviour. There is enough literature on "CAPM doesn't hold". In fact most low beta stocks plot above the security market line (SML). So it would be a mistake to take CAPM so seriously in practice and I would cross question if CAPM works as it is?

In theory, if there are negative interest rates then according to the CAPM equation you would have a negative intercept. Also the market premium would go up by the amount of risk free rate. But this is pure mathematics and one should ask the question, is there value in holding risk-free asset?

In practice, it is wrong to assume CAPM holds even when risk-free rate is positive. Empirically the SML plots with a negative slope, i.e. low beta stocks (value) have higher expected return than high beta stocks (growth). One argument in favour for this is if investors believe in CAPM blindly then they overprice high beta stocks (everyone assume high beta = high return), depleting the "expected return" and under price the low beta stocks increasing the "expected return".

This paper is a good reference to read about low beta anomaly.

-

I would like to note one consequence of negative riskfree rate:

When the riskfree rate becomes more negative, the Market Portfolio (red) converges to the Global Minimum Variance Portfolio (blue).

The Market Portfolio does never equal the GMV Portfolio though, since the slope is infinite.

-