Tuesday, April 21, 2015

Looking Back at Risk Parity's Golden Age

My initial goal of this post was to share why risk parity was less likely to be a free lunch going forward using historical data back to the 1950's (the last time we saw rates at current levels), but it became more of a risk parity 101 piece. I'll save much of those comments for another day.


What is Risk Parity?


Risk parity was a relatively unknown strategy until Bridgewater's All Weather Fund powered its way through the financial crisis ("risk parity" doesn't even show up on Google Trends until 2009). Since that time, the success has spawned numerous imitators. But first... what is Risk Parity?

Per Investopedia:

A portfolio allocation strategy based on targeting risk levels across the various components of an investment portfolio. The risk parity approach to asset allocation allows investors to target specific levels of risk and to divide that risk equally across the entire investment portfolio in order to achieve optimal portfolio diversification for each individual investor. 
The objective of allocating equally to 2+ asset classes by risk is to receive the benefit of diversification and materially improve the Sharpe ratio of a blended allocation.


Backdrop: The Importance of Sharpe Ratios and Correlation

There are two main factors that drive the relative performance of a risk parity allocation vs stocks; (1) the relative Sharpe Ratio of the new asset class introduced (the higher, the better) and (2) the correlation between the new asset class introduced and stocks (the lower, the better).

As a reminder, per Investopedia:
The Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. 
For example…. if cash returns are 2.5%, then stocks returning 10% with a 15% standard deviation has the same 0.50 Sharpe ratio as bonds returning 5% with a 5% standard deviation: 
  • Stocks: (10% - 2.5%) / 15% = 0.50 Sharpe ratio 
  • Bonds: (5% - 2.5%) / 5% = 0.50 Sharpe ratio 
An identical Sharpe ratio means an investor would be indifferent as to whether they held either stocks or bonds (in isolation), irrespective of their risk appetite. If an investor prefers a 7.5% risk target, a 50% stock / 50% cash allocation cuts the initial 15% risk in half, while returning 6.125% (50% x 10% + 50% x 2.5% = 6.125%). Similarly, a bond allocation gets to the same 6.125% return at a 7.5% risk by leveraging up bonds by 50% (150% x 5% - 50% x 2.5% = 6.125%).

If viewed in isolation (if you can only allocate to one asset class), an investor should allocate to the asset class with the highest expected Sharpe ratio, then lever up / down that asset class to match their desired risk target (an either / or question of stocks vs. bonds). Looking at the rolling three-year Sharpe ratio of stocks and bond since 1976, we see that from 1976 through the mid-1990's stocks had consistent positive performance relative to cash (the Sharpe was consistently above zero) and bonds moved largely in sync with stocks. Since the mid 1990's, stocks have had two material periods of negative excess performance, while bonds have provided consistent positive excess return.


Few investors are restricted to holding only stocks and bonds, but many are restricted from applying leverage. For those with the flexibility to allocate to both stock and bonds, as well as apply leverage, correlation between asset classes plays an even greater factor in determining whether the additional asset class should be added, broadening the decision from an initial 'stocks or bonds' question to 'stocks and/or/no bonds' question.

As a reminder per Investopedia:
Correlation is computed into what is known as the correlation coefficient, which ranges between -1 and +1. Perfect positive correlation (a correlation co-efficient of +1) implies that as one security moves, either up or down, the other security will move in lockstep, in the same direction. Alternatively, perfect negative correlation means that if one security moves in either direction the security that is perfectly negatively correlated will move in the opposite direction.
The huge shift in the relationship between stocks and bonds (hugely positive correlation to hugely negative) starting in the late 1990's can be seen in the chart above (the Sharpe ratio of bonds spiked when stocks crashed) and below (a shift that has been hugely beneficial for investors allocating to levered bonds to balance their stock allocation).


Taken together, the mid 1990's started what has been the Golden Age for risk parity. Instead of requiring a high Sharpe ratio in order for bonds to be added a stock allocation, the negative correlation has meant bonds have largely benefited a risk parity allocation even in periods when bonds have materially underperformed stocks.

As a reminder for those that took the CFA and have blacked out all memories, the formula for determining whether a new allocation improves a Sharpe ratio is as follows:

New asset class Sharpe ratio > Current Sharpe ratio x correlation with new asset class

This means that an allocation to bonds makes sense if the Sharpe ratio of bonds > the Sharpe ratio of Stocks x correlation. When correlations are sharply negative, there are much fewer instances when an allocation to bonds won't improve the Sharpe ratio relative to a stock only allocation (something to keep in mind for commodities even if your expected excess return to cash is 0%).

If the figure in the below chart is > 0, an allocation to bonds (at some level) improves the Sharpe ratio. Note that any notional size allocation to bonds may not improve the Sharpe (i.e. a 10% allocation may improve the Sharpe, a 50% allocation may not - see comment section for more of this discussion).



Given the added benefit of materially positive excess performance of bonds relative to cash since the mid-1990's, risk parity has been a home run (in the example below, risk parity is defined as 25% stocks and 75% bonds). These strong results since 1996 coincided with the year Bridgewater launched their All Weather iteration (hats off to Ray Dalio and his timing). As a comparison, predating the Golden Age was a ten year period from 1974-1984 when risk parity underperformed a simple stock allocation, despite an annualized bond return north of 8% (they key being cash yielded even more). Note the slope of the lines below is equal to the Sharpe ratio over each period.


And the rolling results (just look at the widening gap since 1996). Note that the Sharpe ratio for the risk parity portfolio would not change if you lever it (i.e. a 25% stock / 75% treasury allocation has the same Sharpe ratio as a 50% / 150% portfolio).




What now?

On one hand, it isn't all that difficult to outperform interest rates when they're zero. On the other hand, when interest rates do (eventually) move higher, excess returns of bonds will be impacted (treasury rates are currently VERY low per unit of duration). When interest rates do eventually back up, the relative attractiveness of stocks vs. bonds becomes smaller (that case is outlined here), resulting in a higher correlation between stocks and bonds going forward.

This would equate to a one-two punch against the 20-year Golden Age run that risk-parity has enjoyed.

Source: S&P, Barclays