Vineviz, how did you access the Ibbotson Associates data in PortfolioVisualizer?
I'm going to present some data that partly supports, partly contradicts my point of view.
Here's the thing. Yes, of course
it is true that under some
circumstances, and using the MPT/CAPM framework, you can get portfolios with higher Sharpe ratios than any of the portfolio constituents. I get that.
The big question to my mind is this. For the special case of "stocks and bonds," we have robust behavior, due to the fact that they derive their return from fundamentally different sources. It is not just a case of extrapolating from past data. In particular, stocks and bonds have had close to zero correlation--not just imperfect correlation, but seriously low correlation--over just about any time period you look at... while bonds have had an decent positive return over just about any time period you look at. For stocks versus bonds, the diversification benefit virtually always exists and we have high conviction that it will persist going forward. (Indeed, one of the debates is whether we should expect bonds to show negative correlation with stocks, or "merely" zero).
The slice-and-dicers would have us believe that you can get extra, similarly
robust and valuable benefits by looking inside the universe of a single major asset class, stocks, and pulling out subsets of a single asset class--which are then rechristened as "asset classes" in themselves--according to various filtering criteria. And the argument is made that there will almost automatically be improvement as long as the asset classes have "imperfect" correlation, therefore it is almost a sure thing that well-chosen lumpy weighting will improve the portfolio as a whole.
Now, I can't reproduce your example exactly, but pretty close. As you will see, the results I get do not completely confirm my point of view, but they support it partially. My point of view, or bias, is that the MPT magic (the whole is better than any of its parts, measuring by Sharpe ratio) is large and robust for the specific case of stocks and bonds--but tenuous, feeble, and capricious (e.g. with regard to choices of endpoints, indexes, etc.) for subclasses within the major asset classes.
(I have to say, though, that I don't understand how 30-day Treasury bills can have an 0.16 Sharpe ratio. I wonder what source they are using for the "riskless asset?" Oh, OK, I see: "1-month Treasury Bills 1972+" Nope, I still can't get it; if I use CASHX instead of the SBBI bills data I still get a virtually zero Sharpe ratio for bills. Well, never mind. I repeated my analysis using CASHX instead of Treasury bills and the numbers are the same to within roundoff error).
Here's the thing. In your example, you used a 6-way equal weight portfolio of two stock assets and four bond assets. I'm going to claim that most of the improvement can be attributed to the diversification between both stocks and bonds
, and that little of it came from diversification within the stock classes or within the bond classes.
I am getting these Sharpe ratios, 1979 through 2017 inclusive Mine are in square brackets, yours in parentheses. I think they are close enough.
- [0.00](0.16) IA SBBI US 30 Day TBill
- [0.39](0.40) IA SBBI US LT Government
- [0.48](0.46) IA SBBI US LT Corporate
- [0.40](0.47) IA SBBI US IT Government TR
- [0.54](0.52) IA SBBI US Small Stock
- [0.54](0.54) IA SBBI US Large Stock
For your six-way equal-weighted portfolio I get 0.75, you got 0.71.
So I feel that I've reproduced your results pretty well. I'm using annual data; differences might be due to your using monthly data.
However: if I ask "well, what if we just use 33.3% large-cap stocks and 66.7% long-term government bonds," i.e. diversifying between stocks and bonds but not diversifying within either asset class
?" I get 0.64.
So, not using within-class diversification
I still get the result that the portfolio Sharpe ratio is higher than that of any of its components. Just using stocks and bonds adds +0.10 to the Sharpe ratio for stocks. Going to your 6-way split adds an additional +0.11.
Notice that this sort of half-confirms, half-contradicts my point of view. You can spin it either way. For these date endpoints and these data sets, yes, you got an extra increment in Sharpe ratio by using multiple asset subclasses within each asset class.
But in any case, stocks/bonds was a big deal, and just including both stocks and bonds made the whole-is-better-than-any-of-its-parts magic happen.
For a two-way portfolio of large and small stocks, I get 0.58 for the Sharpe ratio. So, in a portfolio of stocks alone, the diversification within stocks adds 0.04 to the Sharpe ratio. Yes, a little magic, but considerably less.
For a four-way portfolio of the four bond classes, I get 0.43 for the Sharpe ratio, which is higher than that two of the constituents (long-term and intermediate-term government) but lower than long-term corporate. The magic did not happen here.
In other words, the MPT-and-Sharpe-ratio case for including both stocks and bonds in portfolios is very good, but the case for departing from the total market portfolio by "diversifying" into lumpy weighting of subclasses within stocks, or with bonds, is much less clear.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.