Financial and International Markets - Coursework Example

Financial and International Markets 2007 Assignment 1: Empirical Evidence on Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) developed independently by Sharpe (1964), Lintner (1965) and Mossin (1966) assumed that asset returns are normally distributed and investors have mean preferences. Hence, it is possible to estimate expected returns, and thus cash flows, by adding an asset to a diversified portfolio. The asset in question is then sensitive to systemic risk (β, beta) as well as the expected return of the market and that of a risk-free asset. This is expressed as [E(Ri) – Rf] / β = E(Rm) – Rf where E(Ri) is the expected risk of the asset, Rf is the risk-free asset, β is the sensitivity of the asset to the market, E(Rm) is the expected return from the market, often assumed to be the return from the market index and [E(Ri) – Rf], the difference between the expected return from the asset and that the risk-free return is the market premium. Thus, risk from adding an asset comprises market risk, or systemic risk, or specific risk, which can be minimized by adding a large number of assets. Thus, theoretically, expected excess return may be estimated by regressing the following equation: [E(Ri) – Rf]t = αit + β [E(Rm) – Rf] - eit The average market return is usually assumed to be the historical return from the market index. Hence, if the coefficient to the historical risk-free asset is estimated to be zero, that is investors can borrow at risk-free rates, then the expected excess return would be estimated to be sensitive to the market risk. However, empirical tests have found that the coefficient to the risk-free asset is not zero. Besides, the model is not directly testable since historical returns may not be the same as future returns, the real structure of the market portfolio may not be known and the market index may not also be an appropriate estimation of the market portfolio (Trandafi). The CAPM model essentially rests on the assumption of normal distribution of asset returns, so that the variance of the returns appropriately measures systemic risk. However, empirical tests have shown that returns may not be normally distributed. Further, investors are assumed to have rational expectations, capital markets perfect and that there are no asset arbitrage possibilities. These assumptions are also suspect and empirical studies have shown that the model may need to be modified substantially when each of these assumptions fail. Fama and French (1992) found that non-market risks and book-to-market value ratios are statistically significant factors that affect asset returns. Following Banz’s (1981) result of firm size on expected returns, Fama and French (1992) found that firm size may be more significant than CAPM (cited in Shackleton & Fergal, 2004). Besides, in contrast to normal distribution of asset returns as assumed by the CAPM model, empirical evidence suggests that probability of extreme returns is higher than normal returns. Thus, the skewness and kurtosis of the distribution of asset returns become significant (Kraus & Litzenberger, 1976 Fang & Lai, 1997, Harvey & Siddiqui, 2000 cited in Shackleton & Fergal, 2004). However, Shackleton and Fergal (2004) found from data of London International Financial Futures and Options Exchange (LIFFE) that systemic variance of returns are significant determinants of a cross section of options contracts while the effect of skewness is less significant. The dynamic asset pricing model depends critically on the joint distribution of the asset prices or returns under study (Singleton, 2006). However, it has often been seen that macroeconomic continuous time-series data is not available. Using discrete time-series data as proxy for continuous data may lead to ambiguous empirical results. In order to modify the unconditional CAPM, following the assertion by Fama and French (1992) that it does not account for the differences in returns on book-to-market values, conditional CAPM models have been proposed. Conditional returns have been estimates as functions of lagged state variables in the multi-factor models (Jagannathan & Wang, 1996, Lettau & Ludvigson, 2001, cited in Adrian & Franzoni, 2006). However, Lewellen and Nagel (2005) insist that although betas vary over time, the relationship between beta and market returns are not strong enough. Adrian & Franzoni (2006) found that since betas are unobservable and vary over time, investors go through a learning process to determine equilibrium expected returns. Estimating returns of 25 portfolios, the study found that conditional CAPM explains variation in returns better that unconditional CAPM that uses Ordinary Least Squares technique to estimate beta. Studies have also proposed downside beta risks as an alternative to systemic beta risks to protect investors from losses (Post and van Vliet, 2004, Hogan & Warren, 2004, Estrada, 2002, Pederson & Hwang, 2003, cited in Galagadera & Brooks, 2005). However, in order to estimate downside risks, only a subset of the data is used and may be biased. Assignment 2: Purchasing Power Parity and the Balance of Payment Approach According to purchasing power parity (PPP), exchange rates of currencies of two countries are in equilibrium when the two currencies can enable the same purchasing power in the two countries. Hence, the exchange rate between the two currencies equals the ratio of prices of a basket of commodities in the two countries. The theory of PPP is based on the “law of one price”, which states that prices of commodities in the two countries are the same when expressed in the same currency, given that there are no transportation and transaction costs. If the prices diverge, there is a process of ‘arbitrage’ between the two countries that tend the prices towards the equilibrium level. For example, if a commodity is lower in Mexico than in the United States, consumers in the US would tend to buy it in Mexico, if there are no trade barriers or transportation costs, bidding up prices in Mexico till it reaches the level as in the US. The “law of one price” may thus be expressed as the following equation: piUS (t) = piMEX t X e (t) where piUS (t) and piMEX t represent the price levels of a particular commodity, i, in the US and Mexico at a point of time and e(t) the nominal (spot) exchange rate between the two countries. If the law holds good for one commodity as well as for the basket of commodities, the PPP may be expressed as: pindexUS (t) = pindexMEX t X e (t) where pindexUS (t) and pindexMEX t where pindexUS (t) and pindexMEX t are a measure of price levels in the US and Mexico respectively. This concept is known as absolute purchasing power parity. However, it is now recognized that absolute PPP does not hold good because of differences in tastes, trade barriers and product differentiation. Even traded goods do not converge towards the absolute PPP because of transportation costs, different tax rates, product differentiation and price discrimination by firms. According to Anderson and van Wincoop (2004, cited in ), such differences are more a rule than exception. To solve this dichotomy, the balance of payments approach, or the relative purchasing power parity is proposed. According to this theory, the exchange rate between the two currencies changes as a result of difference in inflation rates between the two countries. Algebraically, this can be expressed as: ∆ pindexUS (t) - ∆ pindexMEX t = ∆ e(t) where ∆ pindexUS (t) and ∆ pindexMEX t are the inflation rates in the US and Mexico respectively. Intuititively, if inflation rate in Mexico is higher than that in the US, consumers in both Mexico and the US will purchase more commodities in the US, thus bringing down the value of peso till the inflation rates are the same again. In the strictest sense, the exchange rate should be expressed in real terms such that price of Mexican goods in terms of US dollar is the same as the goods in the US against the dollar. Hence, the real exchange rate may be expressed as q (t) = pindexMEX t X e(t) pindexUS (t) Thus, according to relative PPP, real exchange rate tends towards a historical average rate. The real exchange rate adjusts the nominal exchange rate by the price level and signifies the currency’s purchasing power. When the peso rises against the dollar, Mexican exporters are hurt since Mexican goods are more expensive than US goods but imports from the US are cheaper. Thus, the exchange rate as well as the price levels is relevant. In figure 1, the Mexican peso is seen to have faced a drastic depreciation against the US dollar after 1994, after the formation of North America Free Trade Agreement (NAFTA). The nominal value of the Mexican peso is pegged against a basket of currencies. According to Dornbusch and Werner (1994 cited in ), the peso was overvalued prior to the formation of the NAFTA, leading to artificial raising of goods in Mexico and opening up of trade barriers led to the crisis, leading to the fall of relative PPP in Mexico. Since 1988 to 1984, the Bank of Mexico had used the pegged exchange rate to contain inflation, thereby protecting Mexican consumers as well as promoting exports by producers. As a result, however, the Mexican government had to increase borrowings from abroad to finance current account deficits, resulting in capital inflows into Mexico. The NAFTA increased the capital inflows since trade liberalization increased Mexican consumption, reduced the savings rate while increased credit availability boosted personal debt. Higher capital inflows led the peso to appreciate against the dollar drastically, which is evident from the chart. Assignment 3: Validity of PPP as a short run phenomenon According to Dornbusch (1976 cited in Ciboolu, 2002), there may be temporary deviations from PPP as a result of differences in the rate of adjustment in asset and goods markets. While a shock in the money market may change the nominal exchange rate, real exchange rate may remain unchanged because of sticky prices. This “overshooting” of real exchange rate is a reason of deviation from relative PPP in the short run. Besides, foreign and domestic goods may be imperfect substitutes thus preventing the process of arbitrage which may make disturbances in excess demand or supply permanent. If some products, for example houses, are non-tradeable, a change in the relative price between tradeables and non-tradeables results in a change in relative exchange rate that does not tend towards the relative PPP. According to Samuelson (1964) and Balassa (1964), productivity differences lead to a change in relative price between tradeables and non-tradeables (cited in Diboolu, 2002. Empirical studies have shown that nominal and relative exchange rates may remain divergent over the long term (Baillie and Salover, 1987, Taylor, 1988, Baillie and Pecchenino, 1991 cited in Diboolu, 2002). More recent studies have shown that deviations from relative PPP have been the result of relative exchange rate rather than nominal exchange rates. Diboolu (2002) found from studying post-Bretton Woods data that deviations from purchasing power parity are caused by productivity, oil prices and government spending. Deviation from PPP remains even in the long run as a result of productivity differences and differences in growth rates. In figure 2, real exchange rates deviate from the PPP in the short run but over the long run there is a convergence. This is supported by Sideris (2005) who found long run PPP between the US and Germany in a multilateral framework. As opposed to the previous example, in which one currency (peso) is pegged while the other (dollar) is a floating rate, both DM and Dollar are floating exchange rates. Although the short run dynamics are different, it converges over the long run, taking time. Works Cited Harvey, C and Siddique, A (2000). “Conditional Skewness in Asset Pricing Tests”, Journal of Finance. 55, 1263 – 1295 Fang, H and Lai, T (1997). “Cokurtosis and Capital Asset Pricing”. The Financial Review, 32, 293-307 Kraus, A and Litsenberger, R (1976). “Skewness Preference and the Valuation of Risk Assets”. Journal of Finance, 31, 1085-1100 Branz, R (1981). “The Relationship Between Return and Market Value of Common Stocks”. Journal of Financial Economics, 9, 3-18 Mossin, J (1976). “Equilibrium in Capital Asset Market”. Econometrica, 34, 764-783 Lintner, J (1965). “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets”. Review of Economics and Statistics, 47, 13-37 Sharpe, W (1964). “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk”, Journal of Finance, 19, 425-442 Shackleton, M and O’Brien, F (2004). “An Empirical Investigation of UK Option Returns: Overpricing and the Role of Higher Systemic Moments”. Lancaster University Management School Working Paper No 50, 2004, retrieved from http://www.lums.lancs.ac.uk/publications/viewpdf/000302/ Singleton, K.J (2006). Empirical Dynamic Asset Pricing. Princeton University Press http://www.econ.umd.edu/~trandafi/econ435/Chapter_13.pdf Adrian, T and F Franzoni (2006). “Learning about beta: Time-varying Factor Loadings, Expected Returns and Conditional CAPM, Staff Report number 193, Federal Reserve Bank of New York, retrieved from http://www.newyorkfed.org/research/staff_reports/sr193.pdf Jagannathan, R and Z Wang (1996). “The Conditional CAPM and the Cross Section of Expected Returns”, Journal of Finance, 51, 3-53 Lewellen, J and J Shanken (2002). “Learning, Asset Pricing Tests and Market Efficiency”, Journal of Finance, 57, 1113-1145 Galgadera, D.U.A and Brooks, R.D (2005). Is Systematic Downside Beta Risk Really Priced? Evidence in Emerging Market Data. Monash University Department of Econometrics and Business Statistics. Working Paper 11. Retrieved from http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/2005/wp11-05.pdf Diboolu, S (2002). Real Disturbances, Relative Prices and Purchasing Power Parity. Department of Economics, Southern Illinois University of Carbondale. Retrieved from http://129.3.20.41/eps/if/papers/9502/9502002.pdf Dornbusch, R (1976). Expectations and Exchange Rate Dynamics. Journal of Political Economy. 84, 1161-1176 Baillie, R.T and R.A. Pecchenino (1991). The search for equilibrium relationships in international finance: The case of the monetary model. Journal of International Money and Finance, 10, 582-593 Baillie, R.T and D.D. Selover (1987). Cointegration and models of exchange rate determination. International Journal of Forecasting. 3, 43-51 Balassa, B (1964). The purchasing power parity doctrine: A reappraisal, Journal of Political Economy, 72, 584-596 Samuelson, P (1964). Theoretical notes on trade problems, Review of Economics and Statistics. 46, 145-154 Neely, C (1996). The Giant Sucking Sound: Did NAFTA Devour Mexican Peso? Federal Reserve Bank of St. Louis Review, July-August. Retrieved from http://research.stlouisfed.org/publications/review/96/07/9607cn.pdf Sideris, D (2005). Testing for long run PPP in a system context: evidence from the US, Germany and Japan, University of Ionnina Working Paper, retrieved from http://www.econ.uoi.gr/working_papers/Sideris1.pdf Read More