nedsaid wrote: ↑Sun Jan 16, 2022 10:42 am
Seasonal wrote: ↑Sun Jan 16, 2022 10:23 am
I made two points. One was that if you are right that the size effect stopped working because it become too well known, then that should also be true about other well known factors. You did not dispute that. The second is that the market portfolio is the mix of factors that the market regards as appropriate. Note that the market may regard a net zero tilt of a factor as appropriate. You do not appear to dispute that either.
One thing is that you missed is that the calculation of Alpha and Beta have changed. Recall is that Alpha represents excess performance over the benchmark.
It used to be commonly understood that Beta was the volatility of the S&P 500. Today each factor has its own Beta, which does annoy me. So a bond could have a Beta of 1.00 if its volatility matched a bond index, but what I really want to know is how volatile the bond is compared to the stock market. Larry Swedroe and Rick Ferri had a debate about this, Larry was right and Rick was wrong, and a math geek sent me a message and told me Larry was correct. Rick had the old Beta as defined by the S&P 500 set in his mind and it didn't click with him that this all had changed.
So if you run a 3 or 5 factor model, each factor with its own beta, or volatility measurement, then you will get very little Alpha. For a CAPM Model, you could potentially generate a lot of Alpha with active management as the model only predicted 2/3 of the variance in stock returns. Lots of room to generate Alpha. A three factor model accounted for 90% of the variance in stock portfolio returns, an active manager could still generate Alpha but much less. For a 5 factor Model, with each factor having its own Beta, you only have the 4% of variability in stock returns between stock portfolios that the model can't account for, so there is very little Alpha that an active manager can capture.
So instead of one Beta, there are now at least one for each factor in your model. So in a 5 factor model, you have 5 Betas and not just one. You will see this as you analyze portfolios in Morningstar, there is a setting, at least in the professional version, where you can set Beta against the S&P 500 or according to Asset Allocation. So most portfolios, even with a mix of stocks and bonds will have a Beta not too far from one.
You Beta believe it.
It seems like there is an awful lot of text and confusion or muddling of the concept of "beta" here. I'm not sure why each factor having it's own coefficient, or beta, should bother anyone. It's just the mathematical formulation of a return-estimating model. You can't have a factor without a coefficient in a linear model.
I think it's most instructive to just talk about this like a linear model that is predicting returns of some portfolio as a linear function of some variables.
Typically, you can write these as something like y_i = beta*x_i + a, where say you're predicting house prices as y (with house y_i as one observed house), and x is a variable, or factor, that represents the number of bedrooms in the house. So a model is that house_price_i = beta * number_of_bedrooms_i + a. a is a term that represents variation in the house prices that is not captured by the number of bedrooms, like age of house, location, etc.
Turning this into stock prices, now you have (R_i - risk_free_rate) = beta * (R_mkt - risk_free_rate) + alpha. Here, R_i is the return of the investment, and R_mkt is the market portfolio's return.
So if you had a portfolio with a beta of 1, that means your portfolio is fully exposed to the market portfolio, and your returns follow the market portfolio, plus/minus alpha, which is some over- or under-performance relative to the market average, just like you describe.
Now, say you want to include more variables in your model, so instead of just the market return of (R_mkt - risk_free_rate), say you think something like P/E matters for value, and size matters, too. Now you have two new variables, HML for value and SMB for size.
(R_i - risk_free_rate) = beta_mkt * (R_mkt - risk_free_rate) + beta_smb * SMB + beta_hml * HML + alpha.
So in this 3-factor model, yes, we have coefficients for the new factors, because we're trying to estimate how they explain the returns of your portfolio. As you mentioned, it means alpha could be smaller, because these new variables can explain some of your portfolio's returns now. (For example now someone is no longer a magical manager with alpa = 5%, they just created a value portfolio that loaded heavily on beta_hml).
I would disagree though that most portfolios would have a market beta of 1. This is true for most stock-only portfolios, but if you are investing in bonds, your portfolio is not 100% exposed to the equity market anymore. For example if you were 100% VTI, your factor expososures in the 3-factor model above would be close to beta_mkt = 1, beta_smb = 0, beta_hml = 0. Now if you change to a 60/40 portfolio, your factor exposures would be beta_mkt = 0.6, beta_smb = 0, beta_hml = 0.
You would then "pick up" fixed-income factor exposures, because in the same way you can make a linear model to estimate equity returns, you can make a linear model to estimate bond returns. In this case, maybe a simple model is "how much term risk is there" (term), and "how much credit risk is there" (corporate bonds vs treasuries), and that model might look something like R_i = beta_term * duration + beta_credit * (some variable that summarizes credit risk) + alpha