The Perils of Parity May 2010

8/8/2019 The Perils of Parity May 2010

1/16

www.mscibarra.com

MSCI Barra Research 2010 MSCI Barra. All rights reserved. 1 of 16Please refer to the disclaimer at the end of this document.

The Perils of Parity

Investigating the Role of Leverage in Multi-Asset Class Portfolios

May 2010

Oleg Ruban

Dimitris Melas


2/16

The Perils of Parity| May 2010

MSCI Barra Research 2010 MSCI Barra. All rights reserved. 2 of 16Please refer to the disclaimer at the end of this document. RV0310

Introduction

In recent months, several large asset owners reported that they were considering the addition of

leverage to their multi-asset class portfolios. These institutional investors noted that equityallocations introduce more volatility than their overall weighting in a typical multi-asset classportfolio. They argue that a levered fixed income allocation will reduce volatility by reducing equityexposures and increasing allocations to lower returning and lower risk diversifying assets, whilestill meeting expected actuarial returns.

The introduction of leverage to the fixed income allocation is linked to the concept of risk parityportfolios. Proponents of this concept argue that in a well diversified portfolio each asset classshould provide an equal contribution to overall portfolio risk, reducing the potential loss impactfrom any individual asset class allocation.

1

Unlike the traditional approach, where capitalallocation drives the risk of the portfolio, in risk parity portfolios the risk allocation drives thecapital allocation. When a portfolio is constructed using this concept, it is dominated by lowvolatility/low returning assets. As noted by Qian (2005) and Allen (2010), leverage is necessary toachieve the expected return required by institutional investors. To balance the risk profile of a

portfolio, leverage is added to the fixed income allocation.

In this paper, we derive the conditions necessary for a portfolio with a levered fixed incomeallocation to:

a) achieve lower volatility than an unlevered portfolio; andb) achieve a better risk-return profile than an unlevered portfolio.

We show that these conditions define a threshold for correlations between the core unleveredportfolio and the extension levered allocation. For simple two asset class portfolios with equityand fixed income allocations, these conditions can be expressed in terms of correlations betweenequities and bonds. The potential benefits of adding leverage to reduce volatility depends on thecorrelations between bonds and equities, the relative volatility of bonds versus equities, and theweights of the two asset classes in the portfolio. If the goal is to improve the risk-return profile of

the portfolio, the decision to add leverage also depends on the relative Sharpe-ratios of the coreportfolio and the extension. When the portfolio includes only equities and fixed income, we canexamine the problem in terms of relative Sharpe ratios of equities and bonds. We proceed toexamine the empirical plausibility of the derived conditions by looking at the historical behavior ofcorrelations, volatilities, and Sharpe ratios between equities and fixed income. Asset ownersconsidering adding leverage to their fixed income allocation can examine these influences todecide whether negative correlations between bonds and equities, a low ratio of bond to equityvolatility, and higher risk-adjusted returns of bonds relative to equities are likely to persist.

1. Can a Levered Fixed Income Allocation Reduce Portfolio Volatility?

In this section we examine whether adding leverage to the fixed income allocation can reduce

overall portfolio risk. It is important to examine this independent of any return enhancementprovided by a levered fixed income allocation, as risk reduction can be valuable even if the returnof the levered extension is negative. Risk reduction is also frequently cited as the major reasonfor risk parity type strategies.

1For examples, see Qian (2005), Morris and Haeusler (2010).


3/16



Consider an unlevered (long only) reference portfolio with positive weightsB

w in fixed income and

BEww =1 in equities. As shown in the Appendix, adding leverage to the fixed income allocation

lowers portfolio volatility when the correlation between bond and equity returns satisfies:

E

B

E

B

w

wk

+< )1(21

, (1)where kis the leverage coefficient applied to the fixed income allocation (k>1),

E is the volatility

(standard deviation) of the equity allocation, andB

is the volatility of the fixed income allocation.

We see that this correlation threshold becomes more negative as:

1. The leverage coefficient krises;

2. The weight of fixed income in the portfolioB

w rises; and

3. The ratio of bond to equity volatilityEB

/ rises.

For example, assume that a portfolio has an allocation of 50% equity and 50% fixed income, and

the ratio of bond to equity volatility is 3/1/ =EB

(equities are three times more volatile than

bonds). If the fixed income component is levered 2 times, this portfolio will have lower volatility

than the unlevered portfolio only if the correlation between fixed income and equity 5.0


4/16



2. What is the Effect of Leverage on Portfolio Risk-Return Profile?

Qian (2009) argues strongly in favor of building risk parity portfolios noting that backtest resultsshow that in all cases without exception, the Risk Parity portfolios provide Sharpe ratios withhigher long-term returns relative to traditional benchmarks with similar or lower risk. In theAppendix, we show that adding a levered extension to an unlevered core portfolio generallyimproves the portfolios risk return profile (Sharpe ratio) when the gross amount of portfolioleverage Ksatisfies:

UL UU , or( )

XCXXXKr 2+> .

Re-arranging, we obtain

XCX

XK

s

2+> or

+

X

C

XK

s

s 2

+> .

Note thatC

X

C

C

X

X

C

X

s

s

r

r

s

s==

, the ratio of Sharpe ratios of extension and core portfolios.

Therefore

Documents

The Perils of Parity May 2010