A Funny Thing Happened on the Way to the Data Bank Dean Croushore and Tom Stark Understanding Asset Values: Stock Prices, Exchange Rates, And the “Peso Problem” Keith Sill ometimes, the present depends on the future: we can think of, what people expect will hap- Speople carry umbrellas when there is a fore- pen affects how they behave today. Exchange cast for stormy weather; football teams in the rates and prices of assets such as stocks and lead play zone defense late in the game, since bonds depend not only on the most likely future they expect their opponents to pass; advance- outcomes but also on possible but less likely purchase airfares are higher for holiday-travel outcomes. Sometimes a possible outcome can be times, when passenger traffic is expected to be so different from today’s conditions that asset heavy. In each of these cases, and many others prices, which incorporate such extreme possi- bilities, make financial markets look flawed, even if they are not. Economists call such a condition *Keith Sill is a senior economist in the Research De- a “peso problem.” partment of the Philadelphia Fed. No one knows the precise origin of the term 3 BUSINESS REVIEW SEPTEMBER/OCTOBER 2000 peso problem, but it is often attributed to Nobel probabilities of bad (or good!) things happen- laureate Milton Friedman in comments he made ing, model-based forecasts can prove inaccurate about the Mexican peso market of the early and the policy advice that rests on them can suf- 1970s. At that time, the exchange rate between fer. the U.S. dollar and Mexican peso was fixed, as it had been since 1954. At the same time, the inter- PESO PROBLEMS, ECONOMIC est rate on Mexican bank deposits exceeded the FORECASTS, AND EXPECTATIONS interest rate on comparable U.S. bank deposits. Expectations are often an important ingredi- This situation might seem like a flaw in the fi- ent in our everyday actions and decision-mak- nancial markets, since investors could borrow ing. For example, grocery stores become more at the low interest rate in the United States, con- crowded than usual when the weather forecast vert dollars into pesos, deposit the money in calls for a severe snowstorm. Firms may make Mexico and earn a higher interest rate, then con- additional investments in plant and equipment vert the proceeds back into dollars at the same today in order to meet projections of strong fu- exchange rate and pay off their borrowings, ture demand for their products. In the financial making a tidy profit. Friedman noted that the realm, prospects for variables like economic interest rate differential between Mexico and the growth and inflation help determine asset prices United States must have reflected financial mar- and exchange rates. ket concerns that the peso would be devalued. The most useful forecasts give the best ap- Otherwise, the interest-rate differential would proximations of what actually ends up happen- soon disappear as investors increasingly took ing in the economy. We judge the “goodness” of advantage of it. In August 1976, those concerns forecasts by the properties of their forecast er- were justified when the peso was allowed to float rors, which are the differences between a se- against the dollar and its value fell 46 percent. quence of forecasted values of a variable and its The difference in return on comparable U.S. and actual, or “realized,” values. Good forecasts have Mexican assets—which looked like an anomaly forecast errors that are zero, on average. If fore- to analysts who thought the exchange rate cast errors aren’t zero on average, the forecast is would remain fixed because it had been fixed biased: the forecast is more often too high than for 20 years—could be explained once investors’ too low, or vice versa. The presence of bias means recognition of the possibility of a large drop in that the forecaster is repeatedly making the same the value of the peso was factored in. mistake, a mistake we would expect to be elimi- More generally, peso problems can arise when nated as the forecaster learns from his past the possibility that some infrequent or unprec- misses. Good forecasts also have errors that edented event may occur affects asset prices. The aren’t predictable. If they were, the forecast could event must be difficult, perhaps even impossible, obviously be improved by correcting those pre- to accurately predict using economic history. dictable errors. Peso problems present a serious difficulty for economists who like to build and estimate mod- els of the economy and financial markets, then use them to interpret economic data. Empirical 1Calibrating an economic model is a two-step pro- economic models are designed to match features cess. First, the economist must construct a set of mea- of the economy. They are calibrated or estimated surements on economic variables that are consistent with the variables that appear in the model. Second, values using current and historical data on economic must be assigned to the model’s parameters so that the 1 variables. If the historical data used to calibrate behavior of the model economy matches as many fea- or estimate models do not accurately reflect the tures of the constructed data set as possible. 4 FEDERAL RESERVE BANK OF PHILADELPHIA AUnderstanding Funny Thing AssetHappened Values: on Stockthe Way Prices, to the Exchange Data Bank Rates, and the “Peso Problem” Dean Croushore and Tom Keith Stark Sill When the economy is stable, forecasters us- bility of an unusual or unprecedented outcome. ing historical data have a hope of predicting the Indeed, forecasts may look bad despite the fact future with some accuracy. “Stable,” in this con- that forecasters make their estimates using the text, doesn’t mean unchanging. Rather, it means best information at their disposal and the best that the future is similar to the past in that the practices. When peso problems are present, fore- likely occurrence of any future economic outcome casts that look bad may actually be good. is about the same as what we observed in the The Forward Premium Puzzle. Economists past. For example, if people conclude, based on have examined whether peso problems can ac- an analysis of economic history, there’s a 1 per- count for some apparent anomalies in the be- cent chance the stock market will crash in any havior of asset returns. One such anomaly is the given year, they can confidently extrapolate that forward premium puzzle in foreign-exchange analysis into the future if the economy is stable. markets.3 This puzzle is closely related to the But if the economy is unstable, such an extrapo- forecasting issues we have been discussing. lation may not work well. If the economy is not In the foreign-exchange market, investors can stable, people’s beliefs about the likelihood of purchase forward contracts on currencies. A future events may, correctly, be different from forward contract is an agreement to buy or sell a what was observed in the past. currency on a certain future date for a certain Peso problems may occur when the economy future price, called the forward rate. We might faces this sort of instability. In this environment, think that the forward rate would be a good pre- using historical data to predict the future is diffi- dictor of what the spot exchange rate will turn cult because the future may be much different out to be on the day the forward contract ma- from the recent past.2 Wars, nationalizations of tures, since the forward rate is a price that em- industries, and severe political turmoil are ex- bodies financial market participants’ beliefs amples of unusual events that are extremely dif- about the future value of the spot rate. (The spot ficult to predict. But when markets think there is rate is the price at which a currency can be bought a chance such events may occur, that perception or sold for immediate delivery. If you go to your can have a dramatic impact on forecasts and local bank and convert dollars to francs, the con- forecast errors. Forecasts may capture the possi- version takes place at the spot exchange rate.) In bility of unusual events, but until the events ac- an efficient market, the forward rate will equal tually occur, forecasters may seem to make per- the market’s expectation of what the spot ex- sistent errors and their forecasts may look bi- change rate will be when the forward contract ased to someone who is not aware of the possi- matures. The forward rate prediction may be high or low in any given month, but on average, it ought to be correct.4 Economists would then say that the forward rate is an unbiased predic- 2More technically, peso problems can be interpreted tor of the future spot rate. as a failure of the methodology of rational expectations However, when we look at the data, the for- econometrics, which requires that the ex post distribu- tion of economic variables be equal to the expected ex ward rate is not an unbiased predictor of the fu- ante distribution of the same variables. Another way to interpret the peso problem is as a small-sample prob- lem in statistics. If the sample of data is large enough in the sense that the occurrence of rare events in the data 3See the 1994 article by Gregory Hopper for more on coincides with their true likelihood of occurrence, then the forward premium puzzle and the efficiency of the the ex post and ex ante distributions will be the same foreign-exchange market.