Forward earnings yields and equity carry are plausible indicators of risk premia embedded in equity index futures prices. Data for a panel of 25 developed and emerging markets from 2000 to 2018 show that index forward earnings yields have been correlated with market uncertainty across countries and time. Earnings yields have been highest in emerging countries. However, equity carries have not, because they depend on local funding conditions and only indicate the country risk premium that is specific to equity. Both yield and carry metrics display convincing and consistent positive correlation with subsequent index futures returns. Simulations show that for proper equity long-short strategies active volatility adjustment of both signals and positions is essential in order to balance risk premia with the actual state of riskiness of the market.

The post ties in with SRSV’s summary lecture on macro information efficiency, particularly the estimation of fundamental value.

The post is based on proprietary research of Macrosynergy Partners and SRSV Ltd.

### Basic concepts

__Risk premia on equity arise mainly from the simple fact that financial investors are structurally long non-diversifiable equity risk__. The market does not play a zero-sum game. The premium is effectively paid by initial capital owners for the benefit of receiving financing and risk sharing under what is called “asymmetric information” (meaning they know more than most investors). Plausibly, an individual market’s risk premium will be particularly high where and when there is great uncertainty as to earnings prospects and funding conditions. Moreover, an individual stock’s risk premium should depend on company-specific uncertainty as to earnings prospects and its price correlation with non-diversifiable market risk.

Any premium charged on earnings or funding uncertainty should reduce the ratio between price and earnings prospects. Hence, all other things equal, a higher earnings yield should indicate a higher risk premium. However, there are at least __two relevant perspectives on how that risk premium manifests__:

- The first is the perspective of a
**cash investor**. In this case the relevant risk premium is the simple local-currency forward earnings yield, regardless of whether part of that premium may also be receivable in a local-currency fixed-income instrument. - The second is the perspective of a
**leveraged investor**, i.e. an institution that funds positions locally. This includes investors in index futures. The specific equity risk premium paid to this type of investor is the local-currency equity carry. Any risk premium that is incorporated in the local funding rate does not accrue to this type of investor.

While index futures investors only receive the equity premium above the local funding rate (second perspective), the cash perspective may still be relevant. This is because it incorporates a risk premium that attracts flows into local equities, even if it is not specific to the asset class alone. In an extreme case where the local equity market is dominated by cash investors and the local fixed income market is small and illiquid, the forward earnings yield perspective may even be dominant.

A __practical definition of carry across asset classes is return for unchanged market prices__. The advantage of this conventional carry concept is that it is typically related to risk premia and easy to calculate in real time (view post here). This concept is often useful as indicator for risk premia and future excess returns. However, it is fit for such purpose only if the market price on which it is defined does not have a predictable drift. In practice, a valid general carry measure for the purpose of macro trading requires two calculation steps: First one identifies the conventional carry for a specific contract, as defined above. Second, __one adjusts the conventional carry for apparent or plausible price drifts__.

In the case of equity index futures the market convention of carry is the expected dividend yield minus the local short-term funding rate. However, there are at least two plausible sources of price drift. The first is retained earnings and the second is inflation.

- All else equal,
__a company with retained earnings should experience an upward share price drift relative to one without retained earnings__. The theoretical underlying random walk is the price for the existing capital less depreciation. Conceptually, retained earnings add to the existing capital stock. - Inflation is likewise a source of price drift. Conceptually, the index future is a locally-funded equity position. The
__inflation drift arises because a company is a real asset, while local funding rate is nominal__.

As a consequence, __a basic carry measure for equity index futures fit for risk premium trading is the difference between forward earnings yields and the real local funding yield__. This basic carry may be modified further to produce an adjusted carry that is more closely related to risk premia. Such adjustment can be quite comprehensive and could include differentials between capital stock prices and general inflation, differences in forward earnings growth, future drifts in the funding rate and differences in accounting standards.

### An empirical checkup

We have __investigated properties and predictive power of forward earnings yields and real carry for a panel of 25 country index futures with a sample period of 2000-2018__ (August) for most indices. In the exhibits below the market is denoted by market convention of the currency three-letter name. See the list of the names and related index futures at the end of the post. In particular we looked at the following two potential risk premium measures:

- The 12-month forward earnings yield as calculated by IBES based on analyst predictions.
- The real earnings carry, calculated as the difference between forward earnings yield and the real local 1-month interbank rate, whereby “real” means adjustment for a measure of the 1-year forward inflation rate.

Superficially, both measures could be indicators for risk premia. In order to judge their practical use as a trading signal we [1] check whether distributions of these measures across countries and time has been plausible and practical as a trading signal, [2] check correlation with future returns and value generation in naive risk-parity and vol-targeting trading strategies with monthly rebalancing.

### International forward earnings yields and equity carry since 2000

Index averages of forward earnings yields have ranged between 6% and 12% across countries. The mean in the developed world has been 7.2% since 2000. Distributions of forward earnings yields have been very heterogeneous across markets, in both level and variance. __The normal ranges of some country pairs have never overlapped over the sample period, even between similar economies__ (see Malaysia and Korea). The maximum mean distance has been 3.5 panel standard deviations and the widest country standard deviation has been 4.3 times larger than the tightest. All this is consistent with persistent differences in structures and embedded risks of country indices. __The highest forward earnings yields with the widest variations can indeed be seen in EM countries__, particularly Brazil, China, Korea and Turkey.

Real forward earnings carry has been less heterogeneous across countries in mean and just slightly more heterogeneous in variance across countries than forward earnings yields. The carry has almost always been positive. Mostly the __country averages of real forward earnings carry been in a range of 5-10%__. The developed market average has been 6.8%. Only China H-shares have posted an average outside (above) this range. __Risky EM countries have not necessarily offered higher real carry__. Indeed, Brazil and Mexico have recorded the two lowest average real earnings carries globally. This hammers home an important message: in EM countries high local real interest rates can compress the difference between equity and fixed income yields. Thus, even if the earnings yield itself is on the high side, it is not that attractive from a local or leveraged investor perspective due to high opportunity costs.

### Two simplistic long-short strategy signals

We examine the predictive power of forward earnings yields and real earnings-based carry and PnL value creation for naive (most simple and non-optimized) long-short strategies across all 25 country index futures in our panel.

In particular, we examine the value of equity yield and carry for two approaches:

**Risk parity**: The first approach__adjusts trading positions (and their corresponding yield or carry) for relative medium-term standard deviations to the S&P500__. This is a form of risk parity strategy insofar as for equal signals the strategy takes positions that are expected to have roughly equal volatility in the medium term.**Vol targeting**: The second approach__adjusts trading positions (and their corresponding yield or carry signal) for recent individual index price volatility consistent with a 10% annualized volatility target__. Here volatility has two effects: first it sets the signal in negative relation to recent volatility and, second, it reduces unit positions inversely to volatility.

PnL value generation is assessed based on a __naive long-short strategy across: positions are set and rebalanced monthly for all markets, commensurate to the signal’s deviation from its historic panel average__. The latter means that the strategies are coerced to have no directional bias in the long term and thus do not reap the general absolute equity risk premium. It also means that value generated by such naive strategies is conceptually additive to a long-only global equity portfolio.

### Naïve risk parity strategy

__Relative normalization has a material impact on forward earnings yields across countries__. Most importantly, this transformation __makes long-term means of yields more equal across countries__, more so than variances. After normalization high-risk EM countries no longer post the highest averages as relative price volatility has plausibly been correlated with country risk.

There is __strong evidence for persistent positive cross-country correlation between equity indices’ price volatility and forward earnings yields__. Indices with high long-term index price volatility tend to display high earnings yields. The positive correlation has prevailed in every year since 2000. There has been no such clear intertemporal relation. This suggests that both earnings yields and price volatility are subject to common influences, such as macro and market risk factors.

The __probability of positive correlation of normalized forward earnings yields with subsequent monthly normalized returns has been 99%__. The correlation coefficient itself has been 6%. Positive correlation has not been highly reliable: it prevailed intertemporally in 72-80% of all countries (depending on whether one uses parametric or non-parametric estimates) and cross-sectionally in 63-68% of all years. Correlation has been highest in larger developed markets (15% in the U.S. and Germany) and negative in two EM markets (China A-shares and Singapore), possibly related to quality of earnings forecasts.

Alas, despite positive correlation the naive zero-mean strategy would have produced dramatic intermittent drawdowns and just a very small positive Sharpe ratio of 0.22, below the 0.38 of a long-only risk parity portfolio. A combined long-short and long-only portfolio would have produced a Sharpe of just 0.4. __The naive long-short PnL profile underscores a fundamental flaw of this type of trading signal: it is conducive to particular sharp drawdowns in market crises, because forward earnings yields tend to rise sharply when global market or macro risk increases__, due partly to sluggish downward revisions of earnings forecasts.

Real equity carry produced 100% positive correlation probability with subsequent monthly normalized returns and a monthly correlation coefficient of 7%. __Reliability of the positive correlation has been a bit higher than for forward earnings: it prevailed overtime in 84-88% of all markets and cross-sectionally in 68-74% of all years__. The Sharpe ratio based on a zero-mean signal has been 0.42, about double that based on forward earnings yields. Position changes on a monthly basis have been modest and flips infrequent. The direction of positions across countries has typically prevailed for years rather than months. __Correlation has been highest in developed markets (U.S. at 19%, Germany at 16% and UK at 14%)__ and negative in some emerging countries (-10% in China and -8% in Singapore).

The apparent drawback of the normalized carry signal is similar to that of forward earnings yields: it increases long positions when market conditions deteriorate, because real carry increases from the earnings yield and funding rate side. __The principal deficiency is that there is no counterweight to deteriorating macro conditions in that signal__. Hence, when both perceived risk and risk premium increase, this type of signal ignores the former and focuses – myopically – on the latter alone.

### Naive vol-targeting strategy

Vol-targeted forward earnings yields have been quite homogeneous in mean and variance. Regular ranges have been largely overlapping across countries, implying that as a signal this metric leads to more balanced positioning across countries than outright earnings yields.

Introducing volatility targets to signals and positions changes the strategy in two respects.

- First,
__trading signals turn negative with rising volatility__. This means that there is a counterweight to rising earnings yields and carries in times of rising macro risk. - Second, active short-term volatility targeting means that
__positions become more variable overtime__.

The volatility adjustment greatly increases the reliability of forward correlation of the forward earnings ratio-based signal. The probability of positive correlation of vol-targeted forward earnings yields with subsequent monthly returns (on vol-targeted positions) has been 100%. The correlation coefficient itself has been 9%. Reliability has been high: __positive correlation prevailed in 92% of all markets overtime (Italy and South Africa being the only exceptions) and cross-sectionally in 74-84% of all years__, depending on the type of correlation measure used.

__The Sharpe ratio of the naive zero-mean long-short strategy has been 0.72, not considering transaction costs. Unlike the non-targeted strategy it does not experience large drawdowns in crises.__ Note that the volatility-targeting of individual index position has itself been value-enhancing, irrespective of the signal. Thus a long-only book of individually vol-targeted country positions would have produced a long-term Sharpe of 0.6. A combined long-short and long book would have produced a Sharpe ratio of 0.9. Monthly position fluctuations have been considerably larger than without volatility targeting. The directional tendency of individual index positions can still last for many months or even years, but is more often “interrupted”” by short-term directional changes.

Vol-targeted equity carry is still relatively homogeneous in mean and variance, albeit less so than the equivalent forward earnings metric. Classical high-risk EM countries, such as Brazil, China, Mexico and Turkey have recorded below-par averages. This suggests that __equity carry alone does not compensate for riskiness as measured by volatility, plausibly because local rates in these countries also contain premia that accrue implicitly to unlevered investors, but not to holders of index futures__.

__Using real carry rather than aforward earnings yield as basis of the signal further increases the reliability of forward correlation of earnings carry__ and creates even higher naive Sharpe ratios. The probability of positive correlation of vol-targeted forward earnings yields with subsequent monthly returns (on vol-targeted positions) has been 100% with an actual correlation coefficient of 10% (20% for the S&P500 and 18-19% for other large developed markets). __Positive correlation has prevailed intertemporally in 92-96% of countries and cross-sectionally in 79% of all years__.

The naive zero-mean long-short strategy would have produced a long-term Sharpe ratio of 0.75 before transaction costs. This strategy has avoided large drawdowns in past market crises, naturally at the expense of missing some upside in normal times and particular in late-cycle equity rallies with poor valuations and policy tightening. The Sharpe ratio of a combined naive-long short and long-only vol-targeted strategy would have been roughly 1.

### Annex: The 25 markets of the empirical analysis

Futures contracts have been chosen for the following local indices (alphabetically by currency symbol):

AUD: Australian Stock Exchange (ASX) 200 or ASX 200 (200 constituents as of August 2018).

BRL: Brazil Bovespa (67 constituents).

CAD: Toronto Stock Exchange 60 Index (60 constituents).

CHF: Swiss Market or SMI (20 constituents).

CNH: Hang Seng China Enterprises (50 constituents, “H-shares”, actually quoted in HKD).

CNY: Shanghai Shenzhen CSI 300 (300 constituents, “A-shares”).

DEM: Germany DAX 30 Performance/ Xetra (30 constituents, actually quoted in EUR).

ESP: Spain IBEX 35 (35 constituents, actually quoted in EUR).

FRF: France CAC 40 (40 constituents, actually quoted in EUR).

GBP: UK FTSE 100 (101 constituents).

INR: India CNX Nifty (50 constituents).

ITL: Italy FTSE MIB Index (40 constituents).

JPY: Nikkei 225 Stock Average (225 constituents).

KRW: Korea Stock Exchange KOSPI 200 (201 constituents).

MXN: Mexico IPC (35 constituents).

MYR: FTSE Bursa Malaysia KLCI (30 constituents).

NLG: Netherlands AEX Index (25 constituents, actually quoted in EUR).

PLN: Warsaw General Index 20 (20 constituents).

SEK: OMX Stockholm 30 (30 constituents).

SGD: MSCI Singapore Free (25 constituents).

THB: Bangkok SET 50 (50 constituents).

TRY: Turkey Bist National 30 (30 constituents).

TWD: MSCI Taiwan (89 constituents).

USD: Standard and Poor’s 500 Composite (500 constituents).

ZAR: South africa FTSE / JSE Top 40 (42 constituents).

Data for most countries start in 2000-2002.