International Finance and Financial Management - Assignment Example

1. The law of one price s that identical goods should be identically priced in all markets intra and internationally provided there are no impediments to trade like transport costs or differential taxes and the markets are competitive. The law derives from the fact that if identical goods were differentially priced given that there were no trade impediments arbitraging activity would follow with people buying from the cheaper source and selling at the market were the higher price obtained. As a result of such arbitraging, the price would be bid up at the market where the price was previously lower due to a rise in demand while at the same time due to a rise in supply, the price would come down in the market with the higher price and finally as a result of this process the arbitraging would result in equalised prices in all markets. However, it is pertinent to note that there are three conditions required for the law of one price to hold – a) transport costs, transaction costs and other trade barriers should be insignificant. b) All associated markets should be competitive in nature and c) The goods concerned must be tradable. The law of one price does not hold for non-traded goods. This can be illustrated with the following example: Suppose that price of good X per unit is $20 in the US market while it is sold at P (Peso) 150 per unit in Mexico. Suppose the spot exchange rate (Ep/$) is given to be 10 Pesos per Dollar. The dollar price of good X in Mexico can be derived as [P 150 / (Ep/$)] = $15 per unit of X. So in this case, the prices are not yet equalised thereby under insignificant transport costs offering a profitable opportunity of arbitrage in purchasing from Mexico and selling in the US market for a per unit gain of $5. However once such activity burgeons, through the interaction of demand supply forces in the markets, the prices will start moving towards one another so that finally they are equalised provided that the transport and transaction cost barriers do not change due to the increased international arbitraging activity. The law of one price therefore requires the foreign currency denominated price to be equivalent to the home currency price of any domestic good and vice –versa. Thus the law of one price in essence can be translated in to the following equation: PX = e P*X,­ Where PX represents the domestic per unit price of good X, P*X represents the foreign per unit price of good X and e stands for the exchange rate. The law of one price is applicable to the market for foreign exchange as well. Since the exchange rate itself serves as the price in the market for foreign exchange, the law of one price intimates that in the presence of discrepancies in the different domestic prices of particular currencies, the exchange rate itself will adjust to re-establish equilibrium. Otherwise, profitable arbitraging opportunities will remain open. This can be illustrated as follows: Suppose, in a foreign exchange market of Japan, we have: ¥/EURO = 80, ¥/US$ = 100, and ¥/NZ$=50 While in the US exchange market we have: EURO/US$ = 1.3, ¥/US$ = 100 and ¥/NZ$=50 So, evidently, in the USA, NZ$/US$ = 2. So, an individual can sell 2 NZ$ and purchase $1 in USA which he/she then may sell for 1.3 Euro in USA and then with that make a purchase of ¥104 in Japan (Since ¥/EURO = 80 => 1.3 Euro = 80 X (1.3) Yen = 104 Yen). This can be converted in to NZ$ 2.08 as ¥/NZ$=50. So, the individual gains by 0.08 NZ dollars due to the discrepancy. If the mechanism is repeated on a greater scale, presumably, the exchange rates will change so that the currency prices are equalized globally. However, such arbitraging is rarely found as the presence of transaction costs prove to be significantly high enough to render such activity unprofitable. The purchasing power parity theory of exchange rate is in essence an extension of the law of one price with a slight modification. It defines the spot exchange rate as one which equalises the purchasing powers of the related two currencies by translating into the ratio of aggregate price indices of the two associated economies. Purchasing power parity in its absolute form1 implies P = eP* With P and P* representing the domestic and foreign price levels. This is really an aggregative expansion of the law of one price. A simple way to elaborate upon this is to assume two identical commodity baskets B1 and B2 with the subscripts representing the country of origin. Now if the law of one price holds, each good in the commodity basket will be identically priced in terms of a common currency in both nations, i.e, Pi = eP*i where i represents any good present in the commodity basket under consideration. Thus, summing over all i we get P = eP*. Thus we may conclude that the purchasing power parity condition is essentially an extension of the law of one price. 2. The given statement essentially posits the extent of profitability of investing in the shares of a firm that has a highly leveraged capital structure for the shareholders. The degree of veracity of the statement therefore is dependent upon the extent to which the capital structure is relevant for the value generation of the firm concerned. If it is found that a firm with higher financial leverage has higher value compared to a firm with a relatively higher equity to debt ratio, the statement will be established as true. The relevance of the capital structure, i.e, the extent to which any firm finances its assets through debts relative to equities has been a debated issue since the emergence of the irrelevance theorem proposed by Miller and Modigliani (1958b). The theorem implies that in a perfect capital market with no transaction and bankruptcy costs and perfect information if the same interest rate applies to borrowing firms and individuals and there are no taxes imposed, then the capital structure is irrelevant. In other words, under these conditions the debt to equity ratio or the extent of leverage of the firm would have no influence on its value. As an extension of this theorem, it was shown that if corporate incomes were taxed through a classical tax system then higher leveraged firms would generate more value for its shareholders through reducing the tax burden through debt financing. However, this notion can be further expanded to intimate that the optimal capital structure would then be one consisting of no equity and the assets would be entirely financed through debt. Thus the Modigliani-Miller proposition does support the given statement. Though it may seem that the Modigliani-Miller theorem posits that capital structure is not relevant, in essence it implies the exact opposite and also points out the conditions under which the relevance will be significant. In fact the relevance of the capital structure is essentially a derivative of the imperfections that are present in reality in the capital markets. All theories that have exhibited relevance of the capital structure have done so through violating the assumption of perfect capital markets in some particular dimension or another. The major alternative viewpoints can be classified in to two groups – a) trade-off theory and b) Pecking order theory. Trade off theory primarily due to Kraus and Litzenberger (1973) relaxes two of the basic the Modigliani-Miller assumptions and introduces Bankruptcy costs as well as corporate taxes. It is shown that increasing debt financing while being associated with tax benefits also entails the cost of possible bankruptcy. As the extent of leverage increases, the marginal benefit of debt financing declines while the marginal cost rises. Thus the choice of capital structure is essentially an optimality exercise that aims to obtain the highest possible wealth for the shareholders through balancing the tradeoffs. The optimum is attained with the marginal benefit being equated to marginal cost. Thus, if the possibility of bankruptcy is relatively lower to start with so that the optimum is reached with a high debt financing the given statement holds true. However, for a firm that has a relatively higher marginal cost of leveraging that increases at a relatively faster rate compared to the marginal benefit a moderate leverage will be the optimal choice thereby invalidating the given statement. The other alternative theory of optimal capital structure as mentioned earlier is the Pecking order theory propounded by Myers (1984). It departs from the assumption of capital market perfections by introducing asymmetric information. Managers are assumed to be more aware of a firms true position relative to the investors and as a result of this, managers have prefer debts to equities as sources of finance. The theory posits that firms prefer internal debts most as external borrowing may be perceived as a sign of weakness particularly due to the informational asymmetries present and when such sources are depleted they prefer debt financing to equities as issuing new equities may well be regarded as a signal of the fact that managers are attempting to take advantage of some possible overvaluation. Thus the pecking order theory supports the provided statement directly by exhibiting that high debt financing may be optimal in the presence of informational imperfections. 3. a) Expected return on share‘s’ is obtainable as E (rS) = Piri ; where Pi is the probability of the ith state and ri is the associated realised return. Thus, E(rA) = (0.2 x 11%) + (0.4 x 8%) + [0.4 x( -2%)] = 2.2% + 3.2% - 0.8% = 4.6 % And E(rB) = (0.2 x 2%) + (0.4 x 3%) + (0.4 x 5%) = 0.4% + 1.2% + 2% = 3.6% The variance of returns of any share‘s’ can be calculated as S2 =  Pi (ri – E(rS)) 2 Thus, A2 = [0.2 (11% - 4.6%)2 (% - 4.6%)2]+ [ 0.4 (-2% – 4.6%)2]   8.192 + 4.624 + 17.424 = 30.24 Therefore the standard deviation for the returns of A = A = 5.4991 AndB2 = [0.2 (3.6% - 2%)2 (3% - 3.6%)2]+ [ 0.4 (5% - 3.6%)2] = 0.512 + 0.144 + 0.784 = 1.44 => B = (1.2) 3. b) The portfolio return can be computed as a weighted average of the returns of the individual shares. The weights are determined according to the proportion of wealth spent on the respective shares. The Expected return from the portfolio comprising of A and B can thus be obtained as E (R AB) = W A E ( r A ) + W B E ( r B ) = 0.65 X 4.6% + 0.35 X 3.6 % = 4.25. To calculate the return and variance of the portfolio, as a first step we compute the covariance of the returns of the two shares. The covariance of the two shares A and B can be derived as AB =  Pi [rA,i – E(rA)][ rB,i – E(rB)] = [0.2 (11% - 4.6%) (2% - 3.6%)] + [ (% - 4.6%) (3% - 3.6%)] + [0.4 (-2% – 4.6%) (5% - 3.6%)] = -2.048 - 0.816 - 3.696= - 6.56 The next step is to obtain the correlation coefficient between the returns of A and B. It is defined as AB / AB] = (- 6.56) / (5.4991) (1.2) = - 0.9941 The Portfolio variance is obtained as: PORTFOLIO (AB) = (W A A)2 + (W B B)2 + 2AB W A W B = (0.65) (5.4991)2 + (0.35) (1.2)2+ 2 x (- 0. 9941) x (5.4991) (1.2) (0.65) (0.35) = 19.6553 + 0.504 - 2.9848 = 17.2108 Therefore portfolio standard deviation is PORTFOLIO (AB) = 4.1486 3. c) In modern portfolio theory, the efficient frontier is defined as the locus of the portfolios in the expected return- risk space that are considered to be optimal in that either at the corresponding rate of return, the associated risk is minimized through diversification or, alternatively for each associated level of risk, the expected returns are maximised. In mathematical terms the efficient frontier may be defined as the intersection between the minimum variance portfolio set and the maximum expected return portfolio set. Given that the investors are risk averse, higher risk will be tolerated only if the expected return is higher. So, we get a positive slope of the efficient frontier. Further, it is convex as the increase in risk that is tolerated for given increases in expected returns is assumed to be increasing. It has to be noted that the efficient frontier is a combination of all the efficient portfolios which exclude the risk free asset. All portfolios lying below the frontier are suboptimal in that for such portfolio, either a higher expected return can be earned for the same level of risk or for the same expected return the opportunity of bearing lower risk in alternative portfolios exist. 3. d) The risk free asset is essentially a hypothetical asset that pays a rate of return with certainty and thus is ‘risk-free’. Government securities can be thought to resemble a risk-free asset to a significant extent. Thus, by definition the risk-free asset has a zero variance of returns and its returns are uncorrelated to those of any other asset. As a consequence, if the risk free asset is combined with any other asset or portfolio for that matter, the resulting change in return as well as risk is linear. The capital market line is formed by drawing a tangent on the efficient frontier starting from the risk free rate. The line represents different combinations of the risk-free asset with the risky portfolio. The capital market line allows an investor to exceed the bounds imposed by the efficient frontier as combinations on the capital market line offer higher returns for given risks and lower risks for same returns as a rate of return is now incorporated that entails zero risk, for every level of risk the expected return is higher for the combination. So, by combining the risky portfolio with the risk-free asset an investor can construct portfolios with superior risk-return profiles compared to the efficient frontier. 3. d) The tangency point between the efficient frontier and the capital market line is identified as the market portfolio. The unique feature of the market portfolio is that any combination of it with the risk free asset promises a higher return for the same risk than the efficient frontier. It is thus the portfolio with the highest ‘Sharpe ratio’ where the Sharpe ratio is defined as the additional return any portfolio provides for any given level of risk above the risk free rate. References: Kraus, Alan and Litzenberger, Robert, (1973) A State Preference Model of Optimal financial Leverage, Journal of Finance, 28:911–922. Markowitz, Harry M. (1952). Portfolio Selection, Journal of Finance, 7 (1), 77-91. Miller, Merton and Modigliani, Franco. (1958b) The Cost of Capital, Corporation Finance, and the Theory of Investment. American Economic Review, 48:261–297. Myers, Stewart C., (1984) The Capital Structure Puzzle. The Journal of Finance, XXXIX:575–592, Read More