I also updated how I show risk adjusted returns. I think this makes things clearer and more useful at the intuitive level.
To recap: asset class benchmark portfolios (LG,LC,LV,SG,SC,SV) from F-F. Large blend (LB), small blend (SB) and Total Stock Market (TSM) from those benchmark portfolios using monthly market weights. All candidate slice and dice portfolios (blue dots in graphs) are made from all possible combinations using weights that are a multiple of 5% (a computer limitation on my part).
Four particular standard slice and dice portfolios are considered:
4x25: equal parts LB,LV,SB,SV
3x33: equal parts LB,LV,SV
TSM/SV: 60% TSM, 40% SV
LB/SB: 50% LB, 50% SB
Each has significant differences from the other portfolios, and each is similar to portfolio options often encountered in discussions here. The last is included because sometimes due to limitations within someone’s 401K value tilting is not an option, but they have LB and SB options.
One of the things I would like to be able to do is provide some guidance to a novice investor, someone who is not going to run off computing factor weights or want to get into what factor weights even mean. Note that to a naive investor each of the first three Slice and Dice portfolios achieves a similar apparent amount of loading, and as we have seen people often wonder which might be best. Very roughly and very naively:
4x25: 50% value, 50% small, “total tilt” = 100%
3x33: 67% value, 33% small, “total tilt” = 100%
TSM/SV: 40% value, 40% small, “total” tilt = 80% (in fact if one considers the value component of blend and small component of TSM the tilt is a little higher)
LB/SB: 0% value, 50% small, “total” tilt = 50%
The primary results are that:
1) Slice and dice has fairly consistently provided a risk/volatility adjusted benefit.
2) Any two vaguely similar slice and dice portfolios have about the same long term returns and volatility; how you get your tilt does not matter very much, and to the extent that it does, it is not easy to predict ahead of time which tilt is best.
Figure 1: 80 years of asset class returns on top of all possible portfolios formed from the F-F benchmark portfolios and 90-day T-Bills (more on how things change with different types of bonds shortly in another post). Note that averaged over long periods of time a combination of SV and T-Bills is right near the efficient frontier, and SG is about as bad as you can possibly find, and LG is not much better. Given that of all the asset class portfolios, SV has the greatest combined value and small tilt, this should be expected if one averages over enough time; similarly LG should be expected to do poorly. The last place finish for SG has often been noted, but seems a little odd to me relative to the F-F three factor model.
Of course an investor rarely has the luxury of riding out 80 years of ups and down to achieve such results. Figure 2 shows the same information over the four independent 20-year sub-periods. In three of these 20-year periods you can only barely make out a difference between TSM and large growth. Note that TSM is averages about 7% small blend. Even in the period where you can clearly see a difference the difference is not very large. Note too that there are some things that are fairly consistent, such as the position of small value, and some that differ widely such as the position of large growth. The slice and dice portfolios consistently do well, if not quite optimally. The other important thing to note is just the large difference in volatility and return in these periods; you just can’t count on getting an average return even if you buy and hold for 20 years.
However, these graphs do not show how the various standard portfolios compare on a risk adjusted basis. To show this I started with the notion that an investor sets a risk level they are comfortable with, and then they try to build the highest returning portfolio with that level of risk. Here for the sake of user ease I take risk to be volatility.
Suppose someone sets a risk level of standard deviation equal to 15%. Two questions arise: how do you achieve that with each portfolio, and having done that, what is the annual return? With perfect hindsight it is easy to see what level of T-Bills (or bonds) you need to get a standard deviation of 15% over some time period. In this case, over 80 years, you can use 75% TSM and 25% T-Bills, or with the more volatile slice and dice portfolios you need roughly 60% stocks and 40% T-Bills. Note these are fairly aggressive portfolios.
Code: Select all
Percentages to maintain std = 15%
TSM 4x25 3x33 TSM/SV LB/SB
stocks 75% 57% 60% 63% 62%
90-day T-Bills 25% 43% 40% 37% 38%
Figure 3 shows what happens with each portfolio as you dilute it with T-Bills, from zero percent in the upper right to 100% T-Bills in the lower left. The diamonds show the returns at a standard deviation of 15%. I think the most important points are that the value and small slice and dice portfolios run about 1% higher in annual returns if each is held to a standard deviation of 15% (i.e. equal “risk”) compared to the TSM/T-Bill portfolio, and that there is virtually no difference between the three standard value and small slice and dice portfolios on a risk/volatility adjusted basis. The small tilt only portfolio lies between the other slice and dice portfolios and TSM. Note that as an invest sets a lower volatility target the benefit of slice and dice decreases. Also note that costs are not included; if you have significant costs in obtaining the funds needed to tilt your portfolio those costs will reduce any gain in performance.
How consistent is this behavior? Figure 4 shows the same information over the four independent 20-year periods. In one TSM/T-Bills is slightly better than the slice and dice portfolios, otherwise the slice and dice are clearly better. In period one it appears the benefit is all from small, as the LB/SB is as good as any of the value tilted portfolios. In general there is little difference between the three value and small tilted slice and dice portfolios.
I looked at other measures of risk that might be useful to the novice investor, and may report on them later. Things like what happens if you look at 5-year periods, but in the end nothing changed the basic story.