Inflation protected bonds – or “linkers” (short for “price index linked”), as they are affectionately known – are now issued around the world. Investors are starting to consider what place these bonds have in their domestic portfolios, complementing other asset classes such as conventional (“nominal”) bonds and equities. But few have yet confronted the next question: how should I evaluate foreign linkers? Particularly, how do I tell if they are rich or cheap compared with domestic issues?
This article provides a simplified analytical framework for evaluating relative value in index linked bonds. Then we apply this to the real world. The result: it seems hard to reconcile the yield spreads among the world’s index linked bonds with market efficiency and free capital movement. In other words, when we look around the world, some linkers look very rich, others very expensive. One explanation for this is that few investors make international value comparisons among index linked bonds. Because the markets are comparatively young and ill-understood, the world’s index linked bond markets represent a target-rich environment for global value investors. But there are other explanations that don’t involve market inefficiency, and we give examples of these, too.
Table 1 shows some characteristics of the six largest index linked bond markets. While there is wide variation in the size (measured by market capitalisation) of these markets, there are two common properties. First, many index linked bonds have long maturities. Second, most have been introduced only recently. Four of the six largest markets did not exist five years ago.
Suppose that capital was free to flow from country to country without impediment (including different tax treatment for domestic and foreign issues); clientele effects (such as a preference for domestic assets) were unimportant; liquidity and term risk premia were negligible.1 Obviously, that is a lot to swallow. But we can learn about the essential characteristics of index linked bonds by examining them in this austere framework.
In such a world expected returns to index linked bonds in any pair of countries would be equal. Let us consider any two countries – we will call them the US and the UK, and their corresponding currencies dollars and pounds.
From a US investor’s perspective, the real return to an index linked bond (held to maturity) is simply its real yield, as quoted in the market. We will denote this r. The real return to an index linked gilt, again from the US investor’s perspective, is its real yield, denoted r*, plus UK inflation, adjusted for the change in the exchange rate. Simple algebra is all that is needed to show that the gilt’s real return equals its real yield plus an adjustment reflecting the change in the real exchange rate. (The real exchange rate change is that portion of the exchange rate’s change that cannot be explained by differences in the US and UK inflation rates.) If we denote the change in the real exchange rate by x, then
r – r* = x (1)
In other words, this simple model implies that real linker yields should not be everywhere equal. Instead, they should reflect expected future changes in real exchange rates. Equation (1) is the real, or inflation adjusted, version of the uncovered interest rate parity condition, well known in international finance.
Even this simple model yields a potentially testable hypothesis: that international differences among linkers’ real yields substantially reflect overvaluations and undervaluations of their underlying currencies. Countries with undervalued currencies should have linkers with low real yields. Countries with high linker yields should be those with currencies that are overvalued in real terms, and so are expected to depreciate. The low real yield reflects the fact that the holder of an undervalued currency expects it to appreciate through time, in real terms, and that will raise his total return.
To test we need two things. First, we need an estimate of each currency’s long run, “fair” exchange rate. We use Goldman Sachs’ estimates. Second, we need to estimate how quickly a currency’s real exchange rate will return to its fair value. A plausible value is approximately 30% per year. That is, in any year we expect the real exchange rate to adjust by about 30% of its misvaluation. This would imply that effective convergence to fair value would take about five or six years.
Based on these assumptions, we can calculate the expected one-year change in the real exchange rate for each country that issues linkers. If we do the calculation from a US investor’s perspective, the result is shown in figure 1. As you can see, real yields differ considerably internationally. But real yield differences bear no obvious relationship to misalignments in exchange rates. In principal, if our simple model was adequate the observations in figure 1 would line up along a 45° line passing through the origin, and sloping up and to the right. As you can see, they do not. We can illustrate the resulting problem by calculating each bond’s notional expected one year holding period return. Table 2 presents the data.
There are large disparities among expected total returns, when we compare linkers in different countries. Of course, this may simply reflect errors in calculating exchange rates’ fair values, or the assumed dynamics of convergence to their fair rate (30% per year). But using other estimates of fair value, and other convergence rates, produce similar disparities.
Let us summarise the argument so far. If capital markets are efficient and expected real bond returns do not contain risk premia, then real yield differences internationally should be explained by expected real exchange rate changes. It is natural to assume real exchange rates will revert through time toward their fair values. But models based on estimated real exchange rate misalignments cannot explain the pattern of real yield differences we observe in the global bond markets.
In other words, the data are incompatible with real uncovered interest rate parity.
There are two explanations. First, the global market for index linked bonds could be efficient, but there could be tax effects or risk premia embedded in yields that we have not accounted for. Alternately, we could conclude the index linked bond markets are inefficient. Note these explanations are not mutually incompatible – international real yield differences probably reflect elements of both. What could explain rational risk premia in linker yields globally? If linkers have different tax treatment, or different risks, then expected total returns will generally not be equal when we compare linkers in different countries. There are tax and accounting differences internationally, and risks are not identical.
To elaborate on one obvious and observable source of risk, consider linker liquidity. Index linked bond liquidity ranges from poor to terrible. This is a consequence of the small float available in many issues, and the fact that many owners hold their linkers to maturity rather than trade them. So, if you want to execute relative value strategies in linkers – buy a basket of cheap bonds, and simultaneously sell a basket of rich bonds – you would have to be very careful to avoid a forced liquidation of the position.
Trying to buy and sell a large linker position quickly would be expensive. In other words, one reason linker markets may appear to offer unusual opportunities is because an attempt to exploit these opportunities would result in the quintessential “roach motel” trade: you can check in, but you can’t check out.
Now let’s take the other tack. There are plausible reasons to think the global markets for index linked bonds may be more inefficient than the average financial market.
For a starter, many of these markets are relatively young. As Table 1 shows, of the major markets – the US, the Euro-zone and the UK – only two have existed for any appreciable length of time. In the world’s other major economy, Japan, no index linked bond market has yet developed.
Second, in most countries index linked bonds are held by only a few kinds of investors, and these tend to be investors outside the mainstream: (i) they are buy-and-hold investors; that is, they plan to hold the bonds to maturity; (ii) sometimes they do not hold portfolios diversified across many different asset classes; rather, their index linked bonds are held to defese specific inflation linked liabilities; (iii) they generally do not diversify much abroad, and seldom hold any foreign index linked bonds at all. Accordingly, they do not make cross-border comparisons of the prospective total returns accruing to domestic and foreign linkers.
The latter, home country bias, is a well known characteristic of many investors.
Alyce Su is a financial engineer and Lee Thomas is senior international portfolio manager at Pimco in the US