# Late‑Cycle Check: Is Your Asset Allocation Expressing Your Views?

As the economic expansion ages, investors should ensure their portfolios are sufficiently diversified and, importantly, aligned with their own views.

As the economic expansion ages, investors should ensure their portfolios are sufficiently diversified and, importantly, aligned with their own views.

- We use an analytical framework to calculate investors’ forward-looking return estimates for each position in a portfolio, providing an informative “gut check” on whether those estimates are aligned with their own assumptions about markets.
- Given the expected Sharpe ratio (i.e., ratio of return to assumed volatility) for an entire portfolio, we can derive the implied Sharpe ratio (ISR) of each underlying holding.
- Comparing ISRs of various positions can reveal what a given asset allocation is implying about each position’s absolute and relative attractiveness, and ISRs can help us detect correlations across a portfolio. Most importantly, ISRs can help determine if a portfolio’s positioning is aligned with an investor’s actual views.

If we asked investors how stocks are likely to perform relative to bonds, what would they generally say? Historically, stocks have produced higher excess returns^{1} over the long run, both on an absolute and a volatility-adjusted basis. Going forward, stocks are likely to deliver a higher Sharpe ratio (excess return divided by volatility) relative to bonds, as holding stocks involves assuming risk that is correlated with the business cycle. But how much higher will the Sharpe ratio of stocks be versus bonds?

While we can’t ask everyone this question, it turns out one can infer an investor’s relative views from their asset allocation. This topic has been extensively studied in the academic literature on mean-variance portfolio construction,^{2} with the key insight being that the amount of risk allocated to a given asset is related to the expected return of that asset and other correlated assets.

Take, for example, the popular 60/40 stock/bond portfolio, which is a good approximation of many institutional investors’ asset allocation. Given a set of assumptions consistent with long-term market characteristics,^{3} e.g., 16% volatility for stocks, 4% for bonds and a 0% stock-bond correlation, it can be shown that stocks contribute 97% of the estimated excess return above cash, with bonds contributing the remaining 3%. Investors holding this allocation mix are essentially expressing the view that stocks are likely to deliver a Sharpe ratio six times higher than bonds.^{4 }Intuitively, this result should make sense: Why else would investors allocate 97% of their risk budget to a single factor unless they believed it offered a significantly better risk-reward ratio?

As the current economic expansion ages further, we believe asset owners should conduct a thorough analysis to ensure their portfolios are sufficiently diversified and, importantly, *aligned with their own views*.

We walk through an analytical framework that can be used to gauge the level of diversification in a portfolio by estimating the total volatility contribution from each position. This framework can then be used to calculate investors’ forward-looking excess return estimates for each position, providing an informative “gut check” on whether those estimates are aligned with their actual views.^{5}

In a mean-variance-efficient framework, portfolio construction is about the allocation of volatility (i.e., risk), not capital, in a diversified manner. An effective way to gauge diversification in a portfolio is by estimating *net volatility contribution*, which quantifies how much each position contributes to the total portfolio volatility after accounting for its covariance with other assets (i.e., diversification benefits).

The relationship between the net volatility contribution and the stand-alone volatility of an asset is a function of the correlation of the asset’s excess return to the overall portfolio excess return. In particular, for a portfolio containing multiple assets, net volatility contribution of an asset *“s”* is equal to:

*Net Volatility Contribution(s)=Weight(s)×Vol(s)×ρ(s),*

where,

*Weight (s) = Weight of the asset in the portfolio*

*Vol (s) = Volatility estimate for the asset *

* = Estimate of the correlation of the asset “s” with portfolio excess return ^{6}*

The sum of net volatility contribution from all assets in a portfolio mathematically is equal to the overall portfolio volatility. It is important to highlight that if two assets have equal net volatility contributions, it does not necessarily imply the investor has the same level of conviction. In the next section, we will show how investors can determine their implied views on the *relative* attractiveness of various positions in their portfolio.

Calculating the Sharpe ratio for a single asset or risk factor is straightforward: It is the ratio of expected excess return to its assumed volatility. However, coming up with expected Sharpe ratios across complex institutional portfolios isn’t always feasible given they span multiple asset classes, managers and potentially thousands of underlying securities.

But what if the problem were turned on its head? Given the expected Sharpe ratio for the *entire* portfolio, what if one could derive the *implied Sharpe ratio* of each underlying holding? Investors could then use this information to decide if those implied views on risk and reward for each security were congruent with their own thinking. That is exactly what the implied Sharpe ratio (ISR) measure does.

Given a portfolio, the ISR is the implied expected excess return of a given position, *s*, after adjusting for its volatility:

*ISR(s)=Expected Sharpe ratio of the portfolio × ρ(s)*

The correlation, *ρ(s)*, as defined in the previous section, is the ratio of the net volatility contribution of an asset to its stand-alone volatility.

*ρ(s)=(Net Volatility Contribution)/(Weight(s)× Vol (s))*

Under the hypothesis that the portfolio is mean-variance-efficient without any constraints, this ratio is proportional to the ex ante Sharpe ratio of the position. For this reason, the correlation may be interpreted as a measure of an investor’s conviction in active positions.

The ISR measure is elegant as, without any knowledge of investors’ views on macroeconomic conditions, asset valuations or market technicals, it makes it possible to quantify their forward-looking views. In particular, these views can be inferred at any level of granularity, from the level of asset classes, managers, or individual securities, provided we have a sufficiently granular risk model of correlations and volatilities.

Comparing ISRs of various positions can reveal what a given asset allocation is implying about each position’s relative attractiveness. ISRs can be used to size new positions as well as to detect if a certain position is becoming highly correlated with the rest of the portfolio. Most importantly, ISRs can serve as a diagnostic tool to determine if a portfolio’s positioning is aligned with an investor’s own views.^{7}

We now apply the proposed framework above to a hypothetical institutional portfolio to demonstrate how investors can use the ISR measure as a tool for portfolio construction and risk management.

Figure 1 shows a typical policy portfolio of an institutional investor. For the purposes of this exercise and for simplicity, we will assume that this portfolio is expected to deliver a Sharpe ratio of 0.5, though it could be a different number that is more consistent with an investor’s forward-looking view.^{8}

Figure 2 shows the assumed correlation matrix to study this hypothetical example consistent with long-term historical correlations.

When analyzing portfolio volatility, many investors look at the stand-alone volatility of each position, which is simply the product of allocation weight and volatility of the asset. For the sample portfolio, stand-alone volatilities for each asset class are shown in Figure 3.

A quick look at the stand-alone volatilities shows global equities dominate the overall risk profile, followed by private equity, hedge funds and real estate. The assets with the smallest stand-alone volatility are core fixed income and high yield corporate bonds.

Comparing stand-alone volatilities of various assets in a portfolio is a good initial step, but in order to develop a better understanding of the true risk posture, correlations also need to be accounted for. The net volatility takes into account both the size of the stand-alone volatility and the correlation with the overall portfolio. However, while the net volatility shows how much a given position contributes to risk, it does not on its own give us a way to determine if a given allocation should be bigger or smaller. For that type of conclusion, we need the implied Sharpe ratio. The ISR, which is the ratio of net to stand-alone volatility times the portfolio-level Sharpe ratio, shows the Sharpe ratio that investors must be expecting in order to allocate the amount of risk they have to a given position.

We will now illustrate with a few examples how the ISR measure can be used as a metric for assessing portfolio risk and ensuring alignment with investment views.

First, let’s look at the stand-alone volatility of real estate (102 bps) relative to hedge funds (103 bps), as shown in Figure 3. These assets have almost identical stand-alone volatility, but real estate (approximated through REITs) has a higher net volatility contribution (90 bps) than hedge funds (68 bps) because REITs are more correlated with the rest of the portfolio, equities in particular. Since the investor allocated the same level of stand-alone risk to an asset class (REITs) that was more correlated with the rest of the portfolio, the investor must expect that asset (REITs) to deliver a higher Sharpe ratio.

Second, the investor has sized the positions such that hedge funds have a higher net volatility contribution (68 bps) versus high yield (33 bps). This may lead some to prematurely conclude that this investor has a higher conviction in hedge funds because they have more risk allocated to them. However, as shown in Figure 3, the ISR of 0.40 is *higher* for high yield bonds even though they have lower stand-alone and net volatility contributions than hedge funds. The reason for that is high yield bonds are highly correlated to other asset classes in the portfolio, in particular, public and private equity. Therefore, by allocating to them, the investor is loading up on a common risk factor.

From a portfolio construction perspective, an allocation to a highly correlated asset is justified only if the level of conviction is extremely high. Hedge funds are a relatively more diversifying asset and thus have a lower ISR of 0.33. In other words, the bar for allocating to them, and the expected Sharpe ratio they will need to deliver, is much lower. This is why we believe investors need to look beyond stand-alone volatility and net volatility contributions; it is the ratio of these two numbers – the ISR – that matters the most in our view.

Let’s put the ISR measure to further use. Notice that ISR of core fixed income in Figure 3 is slightly negative (−0.03). Bonds tend to be negatively correlated with public equities in most market environments, so they have a small negative net volatility contribution to the overall portfolio. The slightly negative ISR means that investors would have allocated this much risk to core bonds *even if they expected core bonds to have slightly negative excess returns.*

If the investor believes that core bonds are richly valued and that their Sharpe ratios are going to be very negative, then he or she should allocate an even smaller amount to them. On the contrary, if core bonds are estimated to have a positive Sharpe ratio, then they should get a higher allocation, even if that requires using some leverage. The reason is that despite having allocated 15% of market value of the portfolio to core bonds, this allocation is still offsetting the estimated risk in the much larger allocation to equities. The bond allocation is offsetting enough equity risk that it would appear reasonable to allocate to it even if one expected zero returns from core fixed income.^{9}

Let’s look at another example. The ISR of 0.48 for global equities suggests the investor expects them to have the highest Sharpe ratio among assets in the portfolio, and the portfolio is expected to have a high correlation to global equities. Interestingly, asset classes that tend to be highly correlated with equities, like private equity, high yield and real estate, usually also have high ISRs even though their stand-alone volatility is much lower. This should also make intuitive sense as highly correlated assets typically should have similar Sharpe ratios (if not, there should be a great relative value opportunity!).

Coming back full circle, the main question to focus on is whether the investor really believes the Sharpe ratio for core fixed income (with its ISR close to zero) is so much lower than equities (ISR close to 0.5). If that is indeed the investor’s view, then there is nothing further to do in order to align the portfolio’s positioning with that view. If not, the asset allocation needs to be altered so positioning is aligned with the investor’s views.

We use the ISR measure extensively when managing portfolios and sizing positions. We look at ISR both at the individual trade level and at the broad factor or asset class level. When we see a negative ISR we habitually ask, “Should we increase the size of this trade given its diversifying properties?” When ISRs are higher than 0.6–0.7 for multiple positions, we see this as a red flag for potentially insufficient portfolio risk diversification.

In conclusion, the ISR measure is able to encapsulate in a single number an investor’s view of a particular asset, risk factor or trade, and it can be estimated without having any knowledge of the investor’s views on valuations. It has greatly improved the rigor and efficiency of our internal debates on position sizing and portfolio construction, and we believe it is the lens through which investors should approach portfolio construction.

*The authors offer special thanks to Masoud Sharif, PIMCO’s head of portfolio analytics, who has led the effort to refine and implement the ideas expressed in this paper to PIMCO’s portfolios.*

- We use an analytical framework to calculate investors’ forward-looking return estimates for each position in a portfolio, providing an informative “gut check” on whether those estimates are aligned with their own assumptions about markets.
- Given the expected Sharpe ratio (i.e., ratio of return to assumed volatility) for an entire portfolio, we can derive the implied Sharpe ratio (ISR) of each underlying holding.
- Comparing ISRs of various positions can reveal what a given asset allocation is implying about each position’s absolute and relative attractiveness, and ISRs can help us detect correlations across a portfolio. Most importantly, ISRs can help determine if a portfolio’s positioning is aligned with an investor’s actual views.

Portfolio Manager, Commodities

Head of Client Solutions, Americas

Viewpoints
June 2021

This Research paper is a joint effort between PIMCO and GIC, Singapore’s sovereign wealth fund. GIC authors Grace Qiu Tiantian Ph.D., Ding Li, and Zhihui Yap collaborated with PIMCO’s Josh Davis, German Ramirez, and Helen Guo to produce this report.

Blog
# U.S. Equity Values: The Three Dogs That Have Not Barked

Jamil Baz, Josh Davis, Normane Gillmann
March 2021

Thereʼs a bone of contention among investors: Are U.S. equity values about right or far too high?

**The analysis contained in this paper is hypothetical based on a set of assumptions which been provided or illustrative purposes only and are not a prediction or a projection of return**. Actual results may be higher or lower than those shown and may vary substantially over shorter time periods. No representation is being made that any account, product, or strategy will or is likely to achieve profits, losses, or results similar to those shown. Hypothetical or simulated performance results have several inherent limitations. Unlike an actual performance record, simulated results do not represent actual performance and are generally prepared with the benefit of hindsight. There are frequently sharp differences between simulated performance results and the actual results subsequently achieved by any particular account, product, or strategy. In addition, since trades have not actually been executed, simulated results cannot account for the impact of certain market risks such as lack of liquidity. There are numerous other factors related to the markets in general or the implementation of any specific investment strategy, which cannot be fully accounted for in the preparation of simulated results and all of which can adversely affect actual results.

**Figures** are provided for illustrative purposes and are not indicative of the past or future performance of any PIMCO product.

**Correlation** is a statistical measure of how two securities move in relation to each other. The correlation of various indexes or securities against one another or against inflation is based upon data over a certain time period. These correlations may vary substantially in the future or over different time periods that can result in greater volatility.

**All investments **contain risk and may lose value. Investing in the **bond market** is subject to risks, including market, interest rate, issuer, credit, inflation risk, and liquidity risk. The value of most bonds and bond strategies are impacted by changes in interest rates. Bonds and bond strategies with longer durations tend to be more sensitive and volatile than those with shorter durations; bond prices generally fall as interest rates rise, and the current low interest rate environment increases this risk. Current reductions in bond counterparty capacity may contribute to decreased market liquidity and increased price volatility. Bond investments may be worth more or less than the original cost when redeemed.** Equities **may decline in value due to both real and perceived general market, economic and industry conditions.Investing in **foreign-denominated and/or -domiciled securities** may involve heightened risk due to currency fluctuations, and economic and political risks, which may be enhanced in emerging markets. **High yield, lower-rated securities** involve greater risk than higher-rated securities; portfolios that invest in them may be subject to greater levels of credit and liquidity risk than portfolios that do not. **REITs **are subject to risk, such as poor performance by the manager, adverse changes to tax laws or failure to qualify for tax-free pass-through of income. **Alternative investments **involve a high degree of risk that each prospective investor must carefully consider prior to making such an investment. Investors are advised that investment may be suitable only for persons of adequate financial means who have no need for liquidity with respect to their investment and who can bear the economic risk, including the possible complete loss, of their investment. Investors should consult their investment professional prior to making an investment decision.

This material contains the opinions of the manager and such opinions are subject to change without notice. This material has been distributed for informational purposes only and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. It is not possible to invest directly in an unmanaged index. Information contained herein has been obtained from sources believed to be reliable, but not guaranteed. No part of this material may be reproduced in any form, or referred to in any other publication, without express written permission. PIMCO is a trademark of Allianz Asset Management of America L.P. in the United States and throughout the world. ©2019, PIMCO.

This is not an offer of securities to any person in any jurisdiction where it is unlawful or unauthorized. PIMCO provides services only to qualified institutions and investors. No part of this material may be reproduced in any form, or referred to in any other publication, without express written permission. ©2021, PIMCO.

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