Investment pricing models like the CAPM require you to plug in a "risk free" rate of return. This is usually understood to mean the yield on 10-year US Treasury bonds, which are currently <2.4%. However, for an individual investor with a mortgage (or any debt really), the risk-free rate of return is in fact their mortgage rate - e.g. my mortgage rate is about 50% higher than the 10y treasury at 3.625% (and I take the standard deduction, so no adjustment needed). So does a person with debt have a different risk-free rate than the institutional investors they're competing against? Do they have a different required return on an asset?

If I plug my mortgage rate into the CAPM model as my risk free rate, it makes no difference if I invest in the entire market with a beta of 1. At beta=1, the expected return is the historical average return.

Ra - expected return on asset, i.e. the expected ROI you'd require to buy it.

Rf - risk free rate of return

B - beta, a measure of the volatility of the asset's price compared to the market.

Rm - historical return of the market

Ra = Rf + B(Rm - Rf)

E.g.

10% = 2.4% + 1(10%-2.4%)

10% = 4% + 1(10%-4%)

However, at different betas, the numbers start to diverge.

For higher-volatility assets, with beta >1, the expected return on the asset is lower for a person with a mortgage than it is for someone using the 10y treasury as their risk free rate.

17.6% = 2.4% + 2(10% - 2.4%)

16% = 4% + 2(10% -4%)

For low-volatility assets, with beta <1, the expected return on the asset is higher for a person with a mortgage than it is for an investor using the 10 year treasury.

6.2% = 2.4% + 0.5(10% - 2.4%)

7% = 4% + 0.5(10% - 4%)

So the 2 investors do their respective math, and the debt-free investor finds beta = 2 assets to be not worthwhile unless they can expect at least a 17.6% return. The indebted investor, on the other hand, will bite if the return is expected to be at least 16%.

For low-beta assets, it's the opposite. At beta = 0.5, the debt-free investor will buy assets yielding as low as 6.2%, but the indebted investor won't buy unless they expect 7%.

My question is, does this observation mean that investors with a mortgage or other debt should be more inclined to buy risky assets and less inclined to buy low-risk assets? Do they have different security market lines?

At some level, this makes sense. Why buy a 4% corporate bond with some risk when you could just pay down your 4% mortgage at zero risk? Maintaining a big savings account / CD balance while paying a mortgage is also an obvious bad move. However, both investments might make sense for a millionaire with zero debt. Even if both investors have an X% portfolio allocation for risk-free assets, they will make different decisions because the indebted investor has the advantage of a higher-returning risk-free investment. But CAPM implies to me that they should also consider different investments throughout their portfolios.

It's the high-risk observation that throws me off. Should indebted investors be more willing to take higher risks at lower expected returns than debt-free investors? Usually, debt makes people more cautious. Does the math prove that behavioral tendancy a fallacy, or does this mean we should throw out the model?

If this was 1982 and your mortgage rate or treasuries were 15% the model would spit out some illogical outputs, such as buying a 5% yielding investment at beta = 2!

Interesting side note: the CAPM has historically done a poor job predicting actual future returns based on beta. Returns of low-beta stocks have tended to be underestimated. Maybe the lesson is that all this is moot and the model is irrelevant.

https://www.investopedia.com/terms/c/capm.asp