A Funny Thing Happened on the Way to the Data BankDean Croushore and T - PDF document

1 A Funny Thing Happened on the Way to the
A Funny Thing Happened on the Way to the Data BankDean Croushore and Tom StarkUnderstanding Asset Values:heavy. In each of these cases, and many otherspen affects how they behave today. Exchangeso different from today’s conditions that assetbilities, make financial markets look flawed, even 4FEDERAL RESERVE BANK OF PHILADELPHIABUSINESS REVIEWSEPTEMBER/OCTOBER 2000had been since 1954. At the same time, the inter-advantage of it. In August 1976, those concernsagainst the dollar and its value fell 46 percent.More generally, peso problems can arise when occur affects asset prices. Theto accurately predict using economic history.of the economy. They are calibrated or estimateding, model-based forecasts can prove inaccuratefer.FORECASTS, AND EXPECTATIONS Expectations are often an important ingredi-today in order to meet projections of strong fu-ture demand for their products. In the financial The most useful forecasts give the best ap-ing in the economy. We judge the “goodness” offorecast errors that are zero, on average. If fore-too low, or vice versa. The

2 presence of bias meansmistake, a mistake
presence of bias meansmistake, a mistake we would expect to be elimi- A Funny Thing Happened on the Way to the Data BankDean Croushore and Tom Starkfuture with some accuracy. “Stable,” in this con-text, doesn’t mean unchanging. Rather, it meansan analysis of economic history, there’s a 1 per-cent chance the stock market will crash in anygiven year, they can confidently extrapolate thatlation may not work well. If the economy is notfuture events may, correctly, be different fromfaces this sort of instability. In this environment,from the recent past. Wars, nationalizations ofa chance such events may occur, that perceptiontually occur, forecasters may seem to make per- This puzzle is closely related to thepurchase forward contracts on currencies. Afuture price, called the forward rate. We mightor sold for immediate delivery. If you go to yourversion takes place at the spot exchange rate.) Inmatures. The forward rate prediction may be Economists would thenHowever, when we look at the data, the for- not an unbiased predictor of the fu-More technically, p

3 eso problems can be interpreted distribu
eso problems can be interpreted distribu- distribution of the same variables. Another way tolem in statistics. If the sample of data is large enough and distributions will be the same 3See the 1994 article by Gregory Hopper for more onthe forward premium puzzle and the efficiency of the4Assuming investors are risk-neutral. Understanding Asset Values: Stock Prices, Exchange Rates, and the “Peso Problem”Keith Sill 6FEDERAL RESERVE BANK OF PHILADELPHIABUSINESS REVIEWSEPTEMBER/OCTOBER 2000 If foreign-exchange markets thinkthere is some chance the exchange rate will fall,market’s expectation. Research by Martin EvansLet’s look at a simple example. Suppose theper peso. Then the expectation, or expected([0.95 x 20] + [0.05 x 10]). As long as the ex-about devaluation. Someone casually evaluat-making the same mistake over and over. Anis getting things about right. We can then turnthe foreign-exchange market. Risk premiums representholding the asset. See the survey article by Karen LewisHowever, Evans and Lewis find that the peso prob- EXPLANATION OF PESO P

4 ROBLEMSgimes represent different environ
ROBLEMSgimes represent different environments. Aparties. Legislation and fiscal policy might begenerally about the economy’s shifting ran-domly between two (or more) regimes. Examplesthe economy are different from what they are in These disturbances affect eco-nomic variables, so the behavior of variablesstrophic events that may happen only once. The prob-model. If an event is repeated, even infrequently, there isa possibility of its being described statistically. See thethe economy. Examples include dramatic changes in oil A Funny Thing Happened on the Way to the Data BankDean Croushore and Tom Starkquently. We can easily see how this regime-lems. Suppose the economy has been in one re-regime. Their behavior, which reflects their be-bility? We see it in manyvariables. As an example,cessions since World WarII. The economy behavesdifferently in recessionsthan in expansions. Inrecessions, unemploy-consumption drop. In ex-consumption increase.We can think of reces-sions as another, differentregime. Indeed, econo-gime-switching behavior.gime-swit

5 ching is the exchange rate. Research FI
ching is the exchange rate. Research FIGURE 1: Regime Switching and the Exchange Rate Marks per Dollar Exchange RateProbability That Dollar Is in Appreciating RegimeSource: Author's calculationsSource: Author's calculations9See the article by James Hamilton for technical de- Understanding Asset Values: Stock Prices, Exchange Rates, and the “Peso Problem”Keith Sill 8FEDERAL RESERVE BANK OF PHILADELPHIABUSINESS REVIEWSEPTEMBER/OCTOBER 2000mark. My own calculations, using similar meth-ods, confirm their results (Figure 1). The figure’sthe dollar was in the appreciating regime. Thethe dollar was in the appreciating regime. Thethat looks like regime switching. Properly inter-to be biased. Further, the bias will persist untilvised. But persistent bias doesn’t necessarilywrong. It may be that we don’t have enoughcomes that forecasters are considering. If we did,are likely to occur, then use that information tohelp us interpret forecasts. If we had enoughlook unbiased when we used all the data. Good look PESO PROBLEMS, ASSET VALUES,AND FUNDAMENTALScertain

6 future payments could be affected. Tak
future payments could be affected. Takethe case of stock prices. A standard model ofdends are revised up, the price of stock goes up.When expected future dividends are revisedeconomy where peso problems can occur, thegime changes that affect stock prices. In otherhigh. In the “bad” regime, dividend growthtends to be low. It can still be the case that inunusual outcomes. Since stock prices dependIf the regime is good, stock prices will be high. Ifthe regime is bad, stock prices will be low.However, because dividend growth can beeconomy is in at any given time. Therefore, in-gime based on their observations of the economy.economy is in a particular regime. They mayabsolutely certain. This uncertainty means thatdends. The weights reflect the strength of inves- A Funny Thing Happened on the Way to the Data BankDean Croushore and Tom Starkwill be higher. As we have already stated, thisAlternatively, the economy might be in a goodthey previously thought. Dividends in the gooddividends and the bad-regime dividends. SoFinally, new information may affec

7 t investors’that the economy is in the g
t investors’that the economy is in the good regime. Recallthe economy’s current regime. If those beliefsways. Stock prices may jump around even ifthe current regime. Stock-price models may also A striking factthe real appreciation of the stock market. ThePhilippe Jorion and William Goetzmann: the real No country has a higher real returnuniquely high real return to equities? Jorion andeconomy. For example, at the beginning of thecountries, including France, Russia, Germany,Japan, and Argentina. But the stock markets ofall of these countries were interrupted by war,More technically, when peso problems are present,der which peso problems can influence the behavior of 12The real return on equities is measured as the real-ized return from capital gains and dividends minus the Understanding Asset Values: Stock Prices, Exchange Rates, and the “Peso Problem”Keith Sill 10FEDERAL RESERVE BANK OF PHILADELPHIABUSINESS REVIEWSEPTEMBER/OCTOBER 2000 termined by their dividends. But stock prices may haveanother component: a bubble. The bubble theory of stocktheir

8 fundamentals. One type of bubble is a r
fundamentals. One type of bubble is a rational bubble.unrelated to fundamentals. When bubbles are rational,a matter of ongoing research for economists. Some statis-bubbles. Others show that bubble components seem to be One difficulty in testing for bubbles is thateven if they are not really there. Take the case wheredividends are either in a good or bad regime. Suppose thedend) regime. As described in the text, the current price ofit looks like a bubble. Thus, environments in which pesogests are important determinants of stock prices. They includetesting for bubbles. The evidence is mixed. One major problemlar model of asset prices and the presence of a bubble. That is, well. But this event has not occurred,reflected it. The large realized returnrisk. Risk-averse stock market inves-them for the risk of the extreme lossesor political turmoil. The Unitedthat many other countries have. Per-haps, by the luck of the draw, U.S.not to occur.. A very influ-has a peso problem environment. More re-cently, the paper by Jean-Pierre Danthinemium in a p

9 roduction economy. Other re-ing process.
roduction economy. Other re-ing process. These efforts have been less A Funny Thing Happened on the Way to the Data BankDean Croushore and Tom StarkPeso Problems Spell Trouble for Value At Value at risk (VAR) models esti-Financial institutions use VAR models to deter-specific period. A VAR calculation might showexpected to exceed $10 million in a day.VAR models are constructed using historicalportfolio. Because VAR models rely so heavilyproblems are present.returns switches between small-change andlarge-change regimes. If a VAR model is con-returns switch to the large-change regime. A VARregimes. In practice, though, VAR models tendtorical returns most heavily. As we have seen,successful. See the 1996 survey article by Martin EvansVAR models. FIGURE 2: Real Returns on Global Stock MarketsSource: Adapted from Philippe Jorion and William N. Goetzmann, “Global Stock Markets in the TwentiethCentury,” , 54, June 1999, Figure 1. Used with permission. Understanding Asset Values: Stock Prices, Exchange Rates, and the “Peso Problem”Keith Sill 12FEDERAL RESERVE

10 BANK OF PHILADELPHIABUSINESS REVIEWSEPTE
BANK OF PHILADELPHIABUSINESS REVIEWSEPTEMBER/OCTOBER 2000 bution of asset returns. Thus, VAR models maynot accurately estimate the maximum loss a port-folio may suffer.a positive probability to events that might occurdata. Because asset prices embody the financialket inefficiency. Rather, peso problems reflectabout the future. While the peso problem mostcommonly comes up when analyzing foreign-peso problem is that it makes it more difficult topricing anomalies is largely an empirical issue.We have discussed mechanisms by which pesoproblems can potentially affect asset prices. Theeconomic environment is unstable. Smallising but still new. Nonetheless, the literaturecasts about the future behavior of financial vari-ables solely on their recent behavior. 31 (1993), pp. 21-46.Asset Pricing: The Power of the Peso,” PaineWebber Working Paper Series in Money, Economicsand Finance, Columbia Business School, PW-97-19 (August 1998).Engel, Charles, and James Hamilton. “Long Swings in the Dollar: Are They in the Data and Do theAmerican Economic Review,Evans, Mar

11 tin. “Dividend Variability and Stock Mar
tin. “Dividend Variability and Stock Market Swings,” manuscript, New York University Statistical Methods in Finance. Amsterdam: Elsevier, 1996, pp. 613-46.Evans, Martin, and Karen Lewis. “Do Long-Term Swings in the Dollar Affect Estimates of the Risk A Funny Thing Happened on the Way to the Data BankDean Croushore and Tom Stark Hamilton, James. “A New Approach to the Economic Analysis of Nonstationary Time Series and theHopper, Gregory. “Is the Foreign Exchange Market Inefficient?” Hopper, Gregory. “Value at Risk: A New Methodology for Measuring Portfolio Risk,” Review, Federal Reserve Bank of Philadelphia, July/August 1996.Jorion, Philippe, and William Goetzmann. “Global Stock Markets in the Twentieth Century,” JournalKandel, Shmuel, and Robert Stambaugh. “Expectations and Volatility of Consumption and AssetLewis, Karen. “Puzzles in International Financial Markets,” NBER Working Paper No. 4951 (Decem-Rietz, Thomas. “The Equity Premium: A Solution,” , 22 (1988), pp. 117-31. Understanding Asset Values: Stock Prices, Exchange Rates, and the “Peso Problem”Keit