Tuesday, September 27, 2011

Portfolio Allocation

FLG has learned about the efficient frontier, CAPM, and the modern portfolio theory more times than he can count. However, it was only until recently that something clicked for him.

Okay, so here's the key graph:

FLG'll explain a bit. Basically, an investor wants to be up (higher expected return) and to the left (lower risk). The efficient frontier is the boomerang shaped line. It's calculated using covariance matrices between securities, which isn't really all the important for our purposes right now. In fact, ignore everything except the boomerang for right now. What is important is that line represents the best possible set of choices to buy stocks that maximize reward for any particular level of risk. An investor can choose high risk and high return and be at the upper rightmost point on the boomerang. An investor can choose the far leftmost point and have lower risk and reward. Or they could choose anywhere in between based upon their risk tolerance.

To translate this into real world. If you wanted a lot of return and could tolerate a lot of risk, then you'd be mostly in stocks. Conversely, if you wanted low risk, then you'd be mostly in bonds. This echoes standard personal finance advice one reads online, in newspapers, and even on financial company websites.

But that's not all that's on the graph. And this is where FLG, while not quite thrown for a loop, did learn something recently. See where the line hits the vertical axis and it says risk free rate? Good. What's the risk free rate, you ask? Well, it's the return on the risk free asset? What's the risk free asset, you ask? Well, a truly risk free asset doesn't exist and so we use proxies. Many people point to T-Bills and that's what FLG always thought about. But how about if we assumed TIPS to be the risk free asset instead? They have no inflation risk and the default risk, despite the recent unpleasantness, is about as low as one can find on this planet AND unlike T-Bills they come in 5, 10, and 30 year maturities.

Okay, great, FLG. They come in longer maturities and are risk free. What's your point? The point is that the existence of a risk free asset allows an investor to do better than the efficient frontier. Instead, the investor chooses between how much to allocate to the risk free asset and how much to allocate to the portfolio on the efficient frontier that is tangent to the line, i.e. the tangency portfolio. That entire line is higher up and to the left of any point on the boomerang. Thus, the investor is better off.

The choice then is not about how to allocate toward stocks or bonds in one's portfolio, but how much to allocate between TIPS and the tangency portfolio. If an investor is very risk averse, then all TIPS. If they have more risk tolerance, some combination. If they are very risk tolerant and can borrow at the risk free rate, admittedly a questionable assumption for most individuals, then they could take on more risk by allocating greater than 100% of their funds to the tangency portfolio and correspondingly negative portion to the risk free asset to take on more risk.

What does this all mean in real life? What is the tangency portfolio? It means that investors should put the risky portion of their funds in a portfolio diversified internationally and across asset categories by market capitalization, or some approximation thereof keeping costs in mind. And then to manage risk, the investor moves money between that portfolio and TIPS. But that risky portfolio never changes regardless of age or risk tolerance or anything. Nobody should be shifting from stock to corporate bonds to lower their risk.

FLG had learned those models and theories before, but never put two and two together. He already had his portfolio diversified as best he could given costs, but he never really understood how to incorporate TIPS systematically. This makes much more sense.


Andrew Stevens said...

Nobody should be shifting from stock to corporate bonds to lower their risk.

This whole post is about the "one mutual fund theorem," that there is one mutual fund which can be combined with the risk-free asset to make up the whole universe of efficient portfolios. I agree with the quote above, but corporate bonds are a part of the hypothetical one risky fund, as are commodities, real estate, baseball card collections, etc. However, if the proxy you are using for the market portfolio doesn't include corporate bonds, I think that's perfectly okay, just as I think it's perfectly fine to leave out commodities, real estate, and baseball card collections. (I also think it's probably fine if it doesn't include international equities. The S&P 500 is probably a reasonably adequate proxy for the market portfolio, though they would be the first thing I'd add.)

My own portfolio does include corporate bonds, real estate, and commodities, though none of them is very large at all, but I'm an asset class junkie and I justify at least some of my choices as purely for my own entertainment, though I do try to keep the proportions in line with my best guess of what percentage of the market portfolio they make up (certain exceptions made because I also follow the Fama-French three-factor model, though with no real confidence that the hypothetical returns will continue to hold up in the future).

But I've been getting outgunned by the S&P 500 for the last three years (as have you, probably, since my relative losses have been mostly caused by international equities), so I wouldn't advise anybody to emulate me, necessarily.

I do believe that the correct amount of Treasuries in a portfolio for a given risk tolerance is rarely zero. I don't really care that much whether it's TIPS or garden-variety Treasuries. Nobody's been able to convince me that TIPS is substantially better as a risk-free asset proxy.

FLG said...

Just to be clear, my point was about corporate bonds was that if you buy into Tobin's theory, then you don't change your mix between stocks and corporate bonds to lower your risk. Instead, you add more risk free asset to the portfolio.

"Nobody's been able to convince me that TIPS is substantially better as a risk-free asset proxy."

But T-Bills are inflation guaranteed. Sure, they're short maturity and inflation expectations are baked in, but there's no guarantee on the inflation side. With TIPS you are guaranteed a set real return for 5, 10, or 30 years. How is that not better than T-Bills?

FLG said...

BTw, my portfolio consists of either a SP500 or Wilshire 5000 index fund, a MSCI EAFE fund, an emerging market index fund, and a total bond fund, which I think is entirely domestic bonds actually.

Andrew Stevens said...

I knew that's what you were saying about corporate bonds (and I agree with it). I just wanted to clarify why a person might have them since you hadn't included them in your description of the tangency portfolio.

My portfolio is considerably more complex since I have value tilts, small cap tilts, and various other asset classes, such as REITs. This complexity is largely for my own entertainment, though, and I don't advocate such a portfolio for other people. Even assuming that I've done all of my calculations and assumptions right and it all works out fabulously, I'd expect you to get 90-95% of the benefit with your portfolio and do about 1% of the work I do and most people would take that as a very fair trade. (You should see my spreadsheet which calculates what I invest in.)

TIPS are better if you're matching the durations to your expected liability cash flows (i.e. living expenses in retirement). But this is impossible if you're more than 30 years away from retirement since even TIPS has no maturities greater than 30 years, so you are still taking interest rate risk. If you have a large equity tilt in your portfolio (as you and I do), I'm not convinced that you need an inflation hedge in your risk-free asset. If inflation goes hog wild, TIPS will be great and Treasuries will be poor, but your risky portfolio will (likely) keep up with inflation as well and that will do most of the heavy lifting in countering inflation for you. When I'm nearing retirement, I do expect to start duration matching my cash flows, I expect to have much fewer equities in my portfolio as my risk tolerance shrinks (assuming all goes well), and then I expect to be heavily into TIPS assuming they're still around (and, alas, that day is not too far in the future). But for now, I don't think it matters a lot. I have a mix of short duration TIPS in my portfolio as well as short duration Treasuries (and even a short duration international bond fund, though that's a very small overall piece). I have a total bond fund as well, though that was forced on me by restricted investment choices in my daughter's 529 plan (Bonds was where the 529 plan had the comparative advantage, or rather least comparative disadvantage, in cost over my outside investment choices, so I reluctantly allocated some of my bond allocation to the total bond fund. I do treat my daughter's 529 plan as part of my overall portfolio, rather than its own separate portfolio, though that will likely change as she grows older, when I'll have to reallocate.)

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