Value opportunities arise when market prices deviate from contracts’ present values of all associated entitlements or obligations. However, this theoretical concept is difficult and expensive to apply. Instead, simple valuation ratios, such as real interest rates or equity earnings yields with varying enhancements, have remained popular. Moreover, value strategies can take a long time to pay off and positive returns may be concentrated on episodes of “critical transitions”.

Historically, it has been easier to predict relative value between similar contracts rather than absolute value. Also, simple valuation ratios become more meaningful when combined with related economic indicators. Thus, long-term bond yields are plausibly related to inflation expectations and the correlation of bond prices with economic cycles and market trends. Equity earnings yields can be enhanced by economic trends and market information. And effective exchange rates become a more meaningful metric when combined with inflation differentials and measures of competitiveness of a currency area.

This post is the updated summary on “Fundamental Value Estimates” of sr-sv.com.

### The grand theory

In finance, the fundamental value of a security or derivative contract refers to the __expected risk-adjusted present value of all cash flows or, more generally, all associated entitlements or obligations__. Estimating such value conscientiously would require three essential ingredients:

- a specification of all relevant features of the security or contract,
- an appropriate model of the uncertain environment (“stochastic parameters”),
- an asset pricing model that discounts all cash flows or utility to a single present value, under consideration of uncertainty.

This conscientious approach could reveal **value gaps**, differences between the present value and the market price. A contract would be “cheap” if the market price was below the present value and “dear” if it was above. However, this theoretical approach also makes high demands on research, requiring [1] flexible financial modeling skills, [2] advanced statistical inference, and [3] good judgment on what the relevant uncertainties look like (called “priors” in Bayesian analysis). In practice, few institutional investors have the budget, capacity, and know-how for such research, leave alone the patience.

### The humble reality: valuation ratios

The most popular references for “cheapness” or “dearness” of financial assets or contracts are __simple price-based valuation ratios, such as trade-weighted real exchange rates for currencies, real interest rates for fixed income instruments, or earnings yields for equity.__ These simple ratios are easy to understand and monitor in real-time. They also have considerable intuitive appeal. For example, a real trade-weighted exchange rate informs on the effective inflation-adjusted appreciation or depreciation of a currency, which should be in accordance with economic performance and competitiveness. Real interest rates help to assess the plausibility of a particular path of monetary policy rates. And in the equity space, forward earnings yields in relation to real bond yields are a basic sanity check for stock prices.

However, these __simple valuation ratios are not valid approximations for fundamental value gaps__. There is typically a good reason why these valuation ratios are high or low relative to historic averages. The real challenge is to sort the right from the wrong reasons. In other words, judgment on whether valuation ratios are too high or too low depends completely on context. Moreover, because standard valuation ratios are so popular and easy to use, they cannot, by themselves, offer much information advantage. Hence, without further analysis valuation ratios cannot plausibly be a great source of investor value.

### Persistent mispricing and sudden re-pricing

__In the absence of easy and objective valuation metrics, price-value gaps can be wide and persistent__. This inertia may be frustrating for “value traders” but can also offer huge profit opportunities when markets undergo **critical transitions**. Critical transitions are __structural changes in economic backdrop, market regime, and institutions that precipitate a re-evaluation of prices and establish “new trading ranges”__. It is in those times that conscientious estimation of fundamental value pays off. Quantitative signals can help detect when such a transition is underway. The signs include a slowdown in corrections to small perturbations in prices, increased autocorrelation of prices, increased variance and skewness of prices, and a “flickering” of markets between different states. (view post here). The basis of such analysis is **complexity theory**, which describes critical transitions in complex systems and assumes that systems evolve as dis-equilibrium processes

More abstractly __value strategies often produce their highest returns when previous market trends have run their course__ and reverse (view post here). Value and momentum strategies often end up with opposite market views. One strategy succeeds when the other fails. There are two plausible reasons for this.

- First, value investors regularly bet against market trends that appear to ‘have gone too far’ by standard valuation metrics.
- Second, value stocks carry particularly high market risk or ‘bad beta’ and thus fare well when market risk premia are high, and the market turns for the better. This typically coincides with ‘momentum crashes’ in oversold markets.

On the whole, rather than being a stand-alone trading factor or even a rival to trends, value factors are a complement to trend following or momentum strategies.

### Absolute versus relative value

Absolute value means that a contract is cheap relative to its fundamental price estimate. Relative value means that a contract is cheap relative to another contract. It is usually __easier to estimate relative fundamental value across similar contracts rather than absolute fundamental value__. That is because similar types of contracts have most price factors in common and one can concentrate on pricing those that are different. For example, all equity prices in one market have the same stochastic discount factor and all FX forward contracts that are traded against the USD have the same reference currency risks. Indeed, empirical analyses support the intuition that it is easier to predict relative returns within an asset class than to predict absolute returns (view post here). Moreover, directional and relative predictability have been complementary sources of investment returns.

### Fundamental value approaches in the macro space

Value-based investment strategies in the macro space typically focus on a comparison of valuation ratios, such as yields or price ratios, with related economic conditions.

- In the
**fixed income space**,__longer-term yields can be decomposed into expected real rates, real term premia, expected inflation rates, and inflation risk premia__(view post here). A popular approach is “affine term structure models” which stipulate that bond yields evolve over time as an affine function (constant plus linear coefficients) of spot interest rates and a set of stochastic variables. Fundamental value gaps can arise from the mispricing of any of these components.- Often the main challenge is to separate term premia from unbiased forward rate expectations.

__A simple practical approach for estimating future short-term interest rate expectations is to adjust conventional yield curves for so-called “median error curves”,__e. recent historic tendencies of implied future yields to over- or under-predict realized spot yields (view post here). The adjustment produces “neutral curves” or presumed unbiased predictors of future yields. __Term premia are charged for committing to long-term lending or borrowing__. They can be estimated based on term structure models that separate expected short-term rates and risk premia. Such models benefit from the inclusion of macroeconomic variables. In particular, long-term inflation expectations plausibly shape the long-term trend in yield levels. Meanwhile, cyclical fluctuations in inflation and unemployment explain slope and curvature (view post here).__Inflation risk premia are charged for uncertainty regarding future consumer price growth.__They can be positive or negative, depending on whether inflation is expected to be negatively or positively correlated with broad (equity) market returns and economic growth (view posts here and here). A positive correlation of inflation and equity returns means that the inflation risk premia charged on nominal bonds are negative: investors accept a yield discount for negative exposure to inflation, for example as a hedge against deflation.- Fixed income markets evolve in accordance with the economy’s key structural parameters, such as sovereign risk, inflation expectations, and the central bank regime. Hence, models should consider time-varying parameters, time-varying volatility, and even model uncertainty (view post here).

- Often the main challenge is to separate term premia from unbiased forward rate expectations.

- In the
**equity space**,__forward earnings yields are a common and valid basis for fundamental value estimates, particularly if they are adjusted for risk or volatility__(view post here). Earnings yields and differentials between equity dividend yields and bond yields have historically been indicators of misalignments and future stock market corrections (view post here). Unlike fixed-income yields, equity yields are uncertain, not easily predictable, and their interpretation depends upon accounting rules. Indeed, accounting terms, such as investment and book value, are easily misunderstood and confused with similar economic concepts. In particular, accounting values are as much driven by assessment of risk as it is by economic value (view post here).

Estimating__equity value gaps often requires adjusting conventional valuation ratios__. For example, market-wide forward earnings forecasts usually follow price adjustments with a lag, and this predictability can be used to increase the quality of real-time forward earnings yields (view post here). Also, the information value of equity dividend yields can be enhanced by considering other forms of cash returns such as share buybacks and debt redemption to get a broader and more meaningful “shareholder yield” (view post here). Many companies spend a substantial amount of money in share buy-backs and/or debt repayment.

Another popular metric for equity valuation is the market-to-book ratio, which divides a company’s stock market price by its accounting value. The ratio has historically predicted equity returns in the long run. However,__profitability and investment value-added explain most of the variations in the market-to-book ratio and must plausibly be taken into consideration__for investment strategies that are based on market-to-book ratios (view post here). - In the
**foreign exchange space**,__valuation gaps are often based on real____trade-weighted exchange rates__or related metrics. It is intuitive to look jointly at real effective exchange rates and economic performance data. For example, empirical research suggests that real exchange rates that are adjusted for relative productivity growth and product quality differences are indicative of currency overvaluation or undervaluation (view post here). Currency value measures that reflect a country’s competitiveness plausibly have some predictive power for a currency’s future trajectory and its equity market’s relative performance (view post here). Moreover, apparent misalignment of effective exchange rates that go against the desired relative monetary policy stance is a key indicator of FX intervention risk (view post here).

__A complementary indicator to trade-weighted exchange rates is debt-weighted exchange rates__. The latter use weights based on foreign-currency-denominated debt and measure the effect of exchange rate changes on the cost of funding. While trade-weighted depreciation supports economic growth through the “trade channel”, debt-weighted depreciation usually slows economic growth through the “financial channel”, particularly in EM economies (view post here). - In the
**emerging market space**, external current account balances are the most popular indicator of valuation gaps for currencies and local-currency bonds. For example, current account deficits are often used as an indicator of overvaluation and dependence on external financing. However, external balances and cross-border financing are only vaguely related.__Vulnerability to “stops” in financial flows does not depend on trade and capital flows (“net concept”) but only on the volume and origin of financing (“gross concept”)__(view post here). To diagnose “overvaluation” one needs a broad set of competitiveness indicators and to diagnose vulnerability one needs the international investment position.