Thursday, February 27, 2014

Stock/Bond Asset Allocation - Don't bother with duration risk. (Pt. 2)

I want to look some more at asset allocations between stocks & bonds, because I think there might be some subtle but powerful issues to think about here regarding portfolio construction.  (Here's my previous post.) I find evidence that argues while a cash allocation can provide diversification and asset rebalancing benefits, bonds with duration risk have not provided useful downside portfolio risk mitigation, given historical maturity premiums.

More below the fold.

Here, I have graphed the average, maximum, and minimum returns, over the lives of the portfolios, of the 74 portfolios that could have been constructed at the beginning of each year, from 1919 to 1992, with 20 year holding periods.

So, for instance, every portfolio consisting of a 100% allocation to the S&P500 had real returns after 20 years of between 12% and 241%, with an average return of 135%.

For bonds, the range of returns over 20 years was between -74% and 178%, with an average of 43%.

Note that for holding periods of more than 6 years, bonds give absolutely no downside protection in the worst case scenarios.

The 50/50 portfolio does give us some protection.  Diversification significantly lowers the variance of short term portfolios and the benefits of rebalancing boost the average returns.  But, even with these advantages, the downside of holding bonds in long term portfolios outweighs these benefits within 7 years, so that for holding periods longer than that, there is still no benefit from diversifying away from stocks.

Now, understand what I am saying here.  I am not claiming simply that the extra gains from stocks over long periods may not be worth the extra risk they entail.  I am saying that owning any bonds for longer periods than this is suboptimal.  There is no reasonable excuse for owning them.  For a 20 year portfolio, it's like selling call options against a portion of your stock portfolio, and paying the option buyer a 70% negative premium.

The reason is at least threefold:

1) The long term return to bonds does not provide a normal distribution of outcomes.  Bonds have provided bifurcated outcomes with very long persistence.   (See previous post.) See the graph of the annualized standard deviation to the right.  Bonds actually get more risky as the holding period increases, up to about 12 years.  For holding periods longer than that, variance is fairly flat (like a series with random walk tendencies).

2) Stock returns have some serial dependence over short periods, but beyond about 3 years, they have stronger mean reversion tendencies.  Also, while this may be coincidental, over the past century, stocks have tended to follow a 36 year trend pattern, so that as holding periods over this time approach that time frame, variances in holding period returns become very tight, and the variances among the different 20 year portfolios are mostly a reflection of where on that long-term cycle the portfolio was constructed.  While this specific cyclical trend may be spurious, there is little doubt that a financial system that continues to be functional will provide strong long-term mean reversion for equity portfolios.

3) Over long periods the higher average returns from equities overwhelm the effects of variance around these averages.

In the graphs of standard devations and annualized standard deviations, to the right, we can see that mean reversion is stronger for equities, and we can also see that the benefits of the 50/50 portfolio make it preferable to bonds even in the very short time frames.

Keep in mind that using standard deviations biases us toward bonds, because their experienced returns have been so bifurcated and serially correlated.  This is largely why conventional portfolio construction is in error.  If we only look at standard deviations, the 50/50 portolio looks like it always provides some protection.  Even here, after 12 years, bonds are statistically more risky than equities if we measure actual empirical returns over the chosen holding period.  But, as we can see from the worst case scenarios in the graph above (the "min" series of returns), both bonds and diversified portfolios are riskier than equities for holding periods longer than 7 years.

So, a rational portfolio construction would start with 100% cash allocation at negligible holding periods.  As the holding period extends past a year, the cash allocation would be a product of liquidity needs and risk aversion.  The at-risk allocation should be increasingly to stocks as holding periods are extended (more on that below).

Here, I have three graphs that show max, min, and average returns, standard deviations and annualized standard deviations, over 40 year holding periods, for portfolios constructed between 1919 and 1972 and ending between 1959 and 2012.  These behaviors continue even into these longer holding periods.  Note that the worst performing equity portfolios performed better than the best performing bond portfolios for every holding period lasting from 32 to 38 years.

Again, I want to be clear about the extreme point I am making here.  Earlier, I was saying that, at the beginning of a portfolio that will be intact for at least 7 years, using the last 94 years as a guide, while some beginning dates would have had bond portfolios that outperformed stock portfolios, each portfolio construction date would have been presented with a proverbial roll of the dice, where the "stock portfolio" dice were loaded in your favor, so that no rational investor should have included any bonds in their portfolio.  (Choosing between rolling the "bond" dice and the "stock" dice, she would have chosen a handful of "stock" dice, with no bond dice.)

Here I am saying that for portfolios from 32 to 38 years, the dice were so loaded that the "bond" dice had numbers 1 through 4 and the "stock" dice had numbers 5 through 6.  If an investor could have allocated her funds with complete certainty about the holding period outcomes, she would not have put any bonds in any portfolio with a holding period of between 32 and 38 years at any time, ever.

Use Cash Equivalents for short holding periods - not bonds.

What about equities compared to cash?  I constructed these same portfolios using the 1 year interest rate from Robert Shiller's annual data set in place of bonds.  The results are shown in the graphs below.

Here is a comparison of the 3 100% portfolios (100% stocks, 100% long term corporate bonds, and 100% 1 year bills).  The short term bills give a conventional trade-off compared to long-term bonds.  They provide slightly lower returns in exchange for slightly less volatility.  The broad comparisons to equities remain the same, however.

Next is a comparison  with the 50/50 mix.  (The three series here are 100% stocks, 50/50 stocks and long term bonds, and 50/50 stocks and 1 year bills).  Again, cash gives us a more conventional trade-off compared to long-term bonds.  In fact, cash improves the downside risks enough that the 50/50 split does reduce the extreme downside risks compared to a 100% equity portfolio.

As the holding period increases, the benefit on the downside declines, but it never fully disappears.  The 50/50 split is roughly the level where the allocation becomes efficient at the longer holding periods, depending on the investor's risk aversion and liquidity needs.  From this point, as the allocation to equities increases to 100%, the average returns, minimums, and maximums all move toward the behavior of the 100% stock portfolio.

So, while bonds don't provide any benefits to long-term portfolios, there is a non-zero level of cash, invested in short-term, risk-free securities, that provides benefits to portfolios of any duration.  This allocation will be a function of risk aversion.  The fact still remains for longer holding periods that for all but the most risk averse investors, the cash allocation will be minimal.  For shorter holding periods, where a measurable portion of the portfolio would be kept out of equities, some allocation of cash appears to perform at least as well as allocations to bonds with similar downside risks, at all holding periods.

To the left are the cumulative distributions of a 100% stock portfolio and a 50/50 stock/cash (1 year bills) portfolio, for 10 year and 20 year holding periods.  At the 20 year time frame, 100% stocks is clearly the superior choice.  At the 10 year time frame, risk averse investors would allocate some of the portfolio to 1 year bills, but this would come at significant cost in most time periods.

Long Term Corporate Interest Rate minus 3 month Treasury Rate
At historical prices, for a yield-maximizing private investor, duration risk does not appear to add any value to expected portfolio risks and returns.  One caveat I will note is that, if my analysis is correct, markets could correct this by increasing the premium for duration risk.  This is a very noisy data series, but there does seem to be an increasing long term trend in the duration premium, so possibly prices over time will adjust.

On the other hand, if I limit my data to only the period after 1965, the basic relationships don't look like they are different than they are in the longer data.  Real interest rates were especially high in the 1980s and 1990s, and this is reflected in the higher average returns to the bond portfolio, but bonds still haven't provided any long-term downside protection.  More recent time frames than that start to make the number of observations too limited to provide consistent data, but they still don't show any better results for bonds as a hedging tool (except for holding periods of less than 10 years limited to very recent periods).

It will be interesting to see if the next several decades see low real interest rates, with duration spreads that are higher than they had been in the past.  Or maybe there is some other segment of the market that reasonably bids long-duration fixed income up, preventing it from fetching the premium to make it useful in this context.  In the meantime, this sure looks to me like evidence that financial planners should be avoiding duration risk in their clients' portfolios.

Follow up post.

1 comment:

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