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Chapter 33 THE MEXICAN PESO CRISIS FAI-NAN PERNG, The Central Bank of China, Taiwan Abstract The Mexican Peso Crisis was the byproduct of various developments including large inflows of shortterm foreign capital, prolonged current account deficit, and political instability. Between 1990 and 1993, investors in the United States were particularly eager to provide loans, many of them short-term, to the Mexican government and to Mexican corporations. Throughout this period, the share of foreign capital inflows exceeded the current account deficit. However, political instability and U.S. interest rate hikes soon changed the optimism for Mexico’s economic outlook. At the beginning of 1994, this did not affect the value of the peso, for Mexico was operating with a target zone exchange rate and its central bank stood ready to accept pesos and pay out dollars at the fixed rate. Yet Mexico’s reserves of foreign currency were too small to maintain its target zone exchange rate. When Mexico ran out of dollars at the end of 1994, the Mexican government announced a devaluation of the peso. As a result, investors avoided buying Mexican assets, adding to downward pressure on the peso. Overall, the Mexican meltdown of 1994–1995 had many facets. Yet couple of lessons are particularly clear: while foreign capital can make up for the shortfall in domestic saving, only long-term capital – in the forms of foreign direct investment or long-term debt – is conducive to domestic investment; large and abrupt movements of capital across national borders can cause excessive financial market volatility and undermine economic stability in the countries involved. Last and most importantly, prolonged current ac- count deficit should be remedied by allowing the domestic currency to depreciate, promoting savings, or cutting back government expenditure rather than financed by foreign capital inflows. Countries with protracted current account deficits such as Argentina, the Philippines, Indonesia, Thailand, and Saudi Arabia, with Thailand in particular, should heed Mexico’s experience. Keywords: foreign capital inflow; current account deficit; foreign exchange reserves; target zone exchange rate; short-term debt; long-term debt. Mr. Perng, the Governor of Taiwan’s central bank, noted the long running current account deficits for a number of Asian countries in his article published in the Commercial Times on 23 February 1995. He stated that the situation in Thailand was especially worrisome as its current account deficit was mainly financed by shortterm financial capital inflows. Fifteen months after the publication of this article, the Asian financial crisis broke out with Thailand at the front line of the crisis. Fai-nan Perng (Commercial Times, 23 February 1995) The Mexican government stopped repaying external debt obligations in August 1982 due to a shortfall of its foreign exchange reserves. Brazil, Argentina, and Chile followed suit, which triggered what came to be known as the Latin American Debt Crisis. Later, following a series of economic and financial reforms, conditions in Mexico gradually improved sufficiently to start attracting inward in- THE MEXICAN PESO CRISIS vestment again. The debt relief initiative put forth by U.S. Treasury Secretary Nicholas Brady in 1990 eventually put Mexico more firmly back on her feet. Thereafter, Mexico engaged in several rounds of negotiations with the United States with the intent of securing the North American Free Trade Agreement and eventually won the U.S. Congress over toward the end of 1993. It is fair to say that in the years between 1990 and 1993, most foreign investors were bullish about the outlook of the Mexican economy. In a separate development, the advancement of telecommunications and computer technology has sped and immensely reduced the cost of transferring capital. Moreover, a growing number of households started to entrust their savings with professional fund managers. Portfolios managed by fund managers tend to be well diversified with assets invested in multiple currencies (huge sums of money can literally be moved from one currency to another or one financial product to the next at the push of a button), a practice that further hastened the speed and amplified the magnitude of international capital movements (the combined value of cross-border portfolio investment in Europe, America, and Japan reached $2500 billion in 1991). While this was taking place, the U.S. economy was mired in a protracted downturn. The Federal Reserve rightly countered with a monetary stimulus. The interest rate on the three-month fixed deposits was slashed from 10.25 percent in March 1989 to 3.1875 percent in January 1994. Against the backdrop of highly efficient international financial markets, U.S. investors moved a huge chunk of their capital abroad. A significant portion of this outflow was absorbed by emerging markets in Latin America including, of course, Mexico. Owing to the various developments outlined in the preceding paragraphs, substantial foreign capital began to flow into Mexico in 1990. The size of foreign capital inflow ballooned from $8.441 billion in 1990 to $32.06 billion by 1993. Altogether, some $92.647 billion of foreign capital swamped Mexico’s financial markets in those four years (Table 33.1). 611 Among the first to be affected by this foreign capital inflow was, not surprisingly, the Peso. At that time, Mexico’s exchange rate system was one of target zone. The lower bound of the Peso=USD exchange rate had been set at 3.05 since November 1991 when foreign exchange controls were removed. The upper bound had been raised gradually at a rate of 0.0004 Peso per day, beginning on 21 October 1992. The idea was to allow the Peso=USD exchange rate to adjust within a band wide enough to properly reflect supply and demand in the foreign exchange market (Figure 33.1). Before the end of 1993, the Peso=USD exchange rate was relatively stable due to large and sustained foreign capital inflows that more than offset current account deficits. Under this arrangement, the integrity of Mexico’s target zone exchange rate regime was not put to test. At the same time, the Mexican inflation rate was running at a significantly higher level than that of the United States. Between 1990 and September 1994, the U.S. CPI rose by only 4 percent. During the same period, the Mexican CPI jumped by 61.3 percent. In a parallel development, the Peso depreciated from 2.9454 to 3.4040 to a dollar. According to the purchasing power parity, the Peso=USD exchange rate should have been 4.5682 in September 1994. In other words, the Peso was overvalued by 34 percent (Table 33.2 and Figure 33.2). Maintaining a stable Peso=USD exchange rate helped to push the Mexican inflation down, as American prices were stable. Mexican CPI inflation was 23.3 percent in 1990, which dropped to 8.4 percent by September 1994. An overvalued Peso, however, undermined the competitiveness of Mexican exports. It’s a small wonder that the position of the current account continued to worsen. A deficit of $7.451 billion in 1990 swelled to $23.391 billion in 1993, a figure approaching 6 percent of Mexico’s GDP. For 1994, this figure was projected to rise to $28 billion or 8 percent of Mexico’s GDP (Table 33.1). Throughout this period, the share of foreign capital inflows that exceeded the current account deficit was bought by the central bank. This would 612 ENCYCLOPEDIA OF FINANCE Table 33.1. Items 1990 Current Account 7,451 Mexico’s balance of payments (1990–1994) 1991 1992 14,888 24,806 19942 1993 23,391 7,020 (Jan. – Nov.) Trade balance Services Transfers Capital Account 4,433 11,329 6,993 6,305 3,975 2,746 8,441 25,139 20,677 7,150 3,021 27,008 18,891 7,187 2,687 32,059 Direct Investment Portfolio Investment Other Investment Government borrowings Net errors and omissions Reserves and related items1 change in reserve assets ( : increase) Foreign exchange reserves (year end) 2,549 4,742 3,985 12,138 9,877 8,259 1,657 1,454 1,228 2,278 2,218 7,973 3,479 7,834 4,393 19,175 3,440 5,867 5,867 1,745 1,118 4,901 27,867 709 1,136 1,436 7,232 6,129 9,446 17,140 18,394 24,886 16 Dec. 94 11,150 Exchange rate (year end, Peso=US$) 2.9454 3.0710 3.1154 3.1059 13 Jan. 95 3,480 19 Dec. 94 3.4647 22 Dec. 94 4.7000 31 Jan. 95 6.3500 6 Feb. 95 14,600 (Jan. – Nov.) 5.3350 Note: 1. A plus sign indicates a reduction in assets or an increase in liabilities; a minus sign indicates the opposite. 2. As published by Mexico’s central bank in its monetary policy report on 25 January 1995. Source: International Financial Statistics, published by IMF on Jan. 1995. Table 33.2. Nominal exchange rate (Peso=US$) PPP exchange rate (Peso=US$) Whole Sale Price Index (WPI) Mexico Producer Price Index (PPI) US Peso=US$ exchange rate and inflation comparison 1990 1991 1992 1993 1994=9 2.9454 2.9454 100.0 (23.3) 100.0 3.0710 3.5421 120.5 (20.5) 100.2 3.1154 3.9944 136.7 (13.4) 100.8 3.1059 4.2842 148.8 (8.9) 102.3 3.4040 4.5682 163.3 (8.4) 104.0 Note: Annual growth rate % in brackets explain why Mexico’s foreign exchange reserves rose from $5.946 billion in 1989 to $24.886 billion by the end of 1993 (Table 33.1). At the beginning of 1994, for a variety of reasons, investor confidence began to wane. External factors include U.S. interest rate hikes that started from February 1994 and the resulting rise in the rate of return from investing in the dollar, which were inarguably the most important. Explanations that had roots at home include the January 1994 riot in the southern province of Chiapas, the assassination of Señor Colosios, the ruling party’s presidential candidate in March, and the deterioration of the current account deficit. No longer upbeat about the prospect of the Mexican economy and recognizing that the Peso=USD exchange rate had become unstable, foreign capital inflow dried up to a level that could no longer sustain the current account THE MEXICAN PESO CRISIS 613 PESO/US$ 6.5000 6.3750 6.3500 (1/31) 6.2500 6.1250 6.0000 5.8750 5.7500 5.6250 5.500 (12/28) 5.5000 5.3750 5.575(2/10) 5.2500 ) 5.1250 5.0000 4.8750 Actual rate 4.7500 4.6250 4.5000 4.3750 4.2500 4.1250 4.0016(12/21) (upper bound) 4.0000 3.9750(12/21) (actual rate) 3.8750 3.7500 3.6250 3.4712(12/20) (upper bound) Upper bound 3.5000 3.3750 Lower bound 3.3206(12/31) 3.2500 3.0851(11/91) 3.4647(12/20) (actual rate) 3.1543(10/92) 3.1250 3.05 3.0000 1 92 Figure 33.1. 4 7 10 1 93 Peso=US$ exchange rate 4 7 10 1 94 4 7 10 11 12 21 12 01 28 06 95 1 18 1 31 2 10 614 ENCYCLOPEDIA OF FINANCE PESO/US$ 5.0000 4.5000 4.5682 PPP based exchange rate 4.0000 Nominal exchange rate 3.5000 3.4040 3.0000 2.5000 2.0000 1990 Figure 33.2. 1991 1992 1993 1994 1994/9 Nominal exchange rate and purchasing power parity (PPP) based exchange rate deficit. Demand for the U.S. dollar far exceeded the supply in the foreign exchange market; the Peso sapped. In order to keep the Peso exchange rate within the upper bound of the target zone, the Mexican government intervened heavily by selling the dollar, a process that quickly depleted precious foreign exchange reserves. In order to replenish official reserves that were running at a dangerously low level, Mexico issued the Tesobonos, a U.S. dollardenominated short-term debt payable in Peso at maturity. In retrospect, Mexico’s central bank should have tightened its monetary stance. But instead, it acted like an innocent bystander, fearing such measures would dampen economic growth and hoping that foreign investors will return in droves after the presidential election in August. Although the ruling party did get re-elected, its secretary general, Señor Masssieu, was assassinated in September. When the newly elected President Zedillo was sworn into office on December 1, Mexico’s financial markets were on the brink of collapse. Among the many forces that were weighing on Mexico’s financial markets, the overvalued Peso and the accompanying deterioration in the current account deficit were the most obvious. Another key feature of the Mexican debacle was that foreign capital inflows had predominantly been invested in short-term debts. Of the $32 billion worth of capital inflow in 1993, $27.9 billion was invested in such instruments (Table 33.1). The source of this type of foreign capital inflow can be traced to mutual funds (Fidelity alone had $8 billion invested in emerging markets in 1994), and hedge and pension funds. All it took was one telephone call for the funds to be shifted out of Mexico once the fund managers convinced themselves that the Peso exchange rate was unstable or when the sentiment on the outlook of the Mexican economy suddenly turned bearish. With the current account position worsening and the inflow of foreign capital reduced to a trickle, the Mexican government resorted to financing the current account deficit with official reserves in addition to issuing short-term dollar debts and the Tesobonos. Mexico’s foreign exchange reserves declined from $24.886 billion at the end of 1993 to $11.15 billion on 16 December 1994. Although Señor Serra, the finance minister, repeatedly reassured foreign investors that the upper bound of the peso exchange rate would not be breached, that very ceiling was hastily raised from 3.4712 to 4.0016 on 20 December. The Peso exchange rate fell sharply from 3.4647 at the close of the business day on December 20 to 3.9750 the next day, getting uncomfortably close to the 4.0016 mark. Unable to stem the tide of foreign capital outflow and with the level of foreign exchange reserves running precariously low, the Mexican government had little choice but to let the Peso float (Figure 33.1). The Peso fell to an all-time low of 5.5 to a dollar on 28 December. THE MEXICAN PESO CRISIS The exodus of foreign capital not only exerted a severe downward pressure on the Peso exchange rate but also depressed stock prices. The Mexican stock index fell from 2857.5 on 23 September 1994 to 1935.32 on 9 February 1995, or 32 percent in four months (Figure 33.3). For a variety of reasons, the United States came to Mexico’s rescue and brought the international financial community to the negotiating table. Possible explanations for the action taken by the U.S. government include: 1. As much as $53 billion of debt was about to become due at the end of 1995. Unaided, Mexico was in eminent danger of repeating the 1982 crisis. 2. Mexico had become United States’ third largest trading partner, with bilateral trade amounting to $100 billion per annum. A further deterioration in the Mexican economy was more than likely to have a negative impact on the United States; the number of illegal immigrants waiting to cross the border could rise considerably. 615 4. The aid package included broad based economic stabilization measures (putting a 7 percent cap on wage increases, cutting back government expenditure, and curbing the expansion of bank credits and money supply). President Bill Clinton’s proposal to provide a $40 billion loan guarantee that would have enabled Mexico to raise fresh capital in international financial markets and resume debt repayment was rejected by the U.S. Congress on 30 January. The Peso took the hit and tumbled to 6.35 to a dollar the next day. By then, Mexico had only enough foreign exchange reserves to last two more days. In an emergency session, the United States, Germany, and France finally agreed to provide Mexico with a $48.8 billion refinancing package, the details of which are as follows: 1. The U.S. government would establish a $20 billion credit line (with $1.4 billion coming from the Exchange Stabilization Fund of the Department of Treasury) made up of: (a) A Peso=dollar swap line for maturities that fall within 12 months or between 3 to 5 years 3. The contagion effect of the Mexican crisis was beginning to be felt by other large Latin American debtors such as Brazil and Argentina. Helping Mexico would prevent the contagion from spreading further afield. (b) Guarantee for debts with maturities up to 10 years designed to help Mexico to raise new debts in international markets. 3000 2857.52 (9/23) 2800 2600 2596.16 (11/19) 2409.2 (12/29) 2400 2200 2000 1800 9/1 9/14 1994 Figure 33.3. Mexican stock index 2416.67 (11/23) 2203.67 (12/21) 1972.33 (1/10) 1935.32 (2/9) 9/28 10/11 10/24 11/8 11/21 12/5 12/19 12/30 1/12 1/25 2/7 2/9 1995 616 ENCYCLOPEDIA OF FINANCE The remaining $600 million came in the form of a temporary short-term swap credit line set up by the U.S. Federal Reserve. 2. The IMF offered a $17.8 credit line of which $7.8 billion came in the form of emergency credits and a $10 billion stand-by credit facility financed by emerging market economies with ample foreign exchange reserves. 3. The Bank for International Settlements chipped in with a $10 billion credit line consisting of swap facilities offered by its 29 member central banks (including the United States, Japan, Germany, UK, and France). 4. Argentina, Mexico, Chile, and Colombia collectively offered a $1 billion credit line. The combined value of the four credit lines listed above summed to $48.8 billion. Meanwhile, a consortium of private sector financial institutions headed by Citibank and JP Morgan negotiated for a syndication loan worth $3 billion. The following lessons can be learnt from the Mexican financial crisis: I. Capital formation can promote economic growth, but the most reliable source of fund is domestic savings. While foreign capital can make up for the shortfall in domestic savings, only long-term capital, in the forms of foreign direct investment or long-term debt, is conducive to domestic investment. Foreign portfolio investment channels funds into secondary markets, resulting in the transfer of ownership, but brings little direct benefit to domestic capital formation. II. The size of global portfolio investment has grown exponentially. Fund managers make investment decisions based on predictions about future exchange rates, interest differentials, and stock prices. Large and abrupt movements of capital across national borders can cause excessive financial market volatility and undermine economic stability in the countries involved. These adverse effects would be especially acute in small but highly open economies. For this reason, capital account liberalization should follow a gradual and orderly approach. III. Prolonged current account deficit should be remedied (by allowing the domestic currency to depreciate, promoting saving, or cutting back government expenditure) rather than financed by foreign capital inflows. A country cannot rely on external financing indefinitely. Interestingly enough, countries like Argentina, the Philippines, Indonesia, Thailand, and Saudi Arabia have all been running current account deficits since 1987. It is worth pointing out that Thailand, in particular, relies almost exclusively on short-term capital inflows to finance her current account deficit. IV. The IMF should acquire in-depth knowledge of member economies, work with them to establish an early warning system, and make policy recommendations that would prevent the outbreak of future crises. Chapter 34 PORTFOLIO PERFORMANCE EVALUATION LALITH P. SAMARAKOON, University of St. Thomas, USA TANWEER HASAN, Roosevelt University, USA Abstract The portfolio performance evaluation involves the determination of how a managed portfolio has performed relative to some comparison benchmark. Performance evaluation methods generally fall into two categories, namely conventional and riskadjusted methods. The most widely used conventional methods include benchmark comparison and style comparison. The risk-adjusted methods adjust returns in order to take account of differences in risk levels between the managed portfolio and the benchmark portfolio. The major methods are the Sharpe ratio, Treynor ratio, Jensen’s alpha, Modigliani and Modigliani, and Treynor Squared. The riskadjusted methods are preferred to the conventional methods. Keywords: performance; evaluation; standard deviation; systematic risk; conventional methods; benchmark comparison; style comparison; riskadjusted measures; Sharpe measure; Treynor measure; Jensen measure; alpha; Modigliani-Modigliani measure; Treynor squared 34.1. Introduction The portfolio performance evaluation primarily refers to the determination of how a particular investment portfolio has performed relative to some comparison benchmark. The evaluation can indicate the extent to which the portfolio has outperformed or under-performed, or whether it has performed at par with the benchmark. The evaluation of portfolio performance is important for several reasons. First, the investor, whose funds have been invested in the portfolio, needs to know the relative performance of the portfolio. The performance review must generate and provide information that will help the investor to assess any need for rebalancing of his investments. Second, the management of the portfolio needs this information to evaluate the performance of the manager of the portfolio and to determine the manager’s compensation, if that is tied to the portfolio performance. The performance evaluation methods generally fall into two categories, namely conventional and risk-adjusted methods. 34.2. Conventional Methods 34.2.1. Benchmark Comparison The most straightforward conventional method involves comparison of the performance of an investment portfolio against a broader market index. The most widely used market index in the United States is the S&P 500 index, which measures the price movements of 500 U.S. stocks compiled by the Standard & Poor’s Corporation. If the return on the portfolio exceeds that of the benchmark 618 ENCYCLOPEDIA OF FINANCE index, measured during identical time periods, then the portfolio is said to have beaten the benchmark index. While this type of comparison with a passive index is very common in the investment world, it creates a particular problem. The level of risk of the investment portfolio may not be the same as that of the benchmark index portfolio. Higher risk should lead to commensurately higher returns in the long term. This means if the investment portfolio has performed better than the benchmark portfolio, it may be due to the investment portfolio being more risky than the benchmark portfolio. Therefore, a simple comparison of the return on an investment portfolio with that of a benchmark portfolio may not produce valid results. 34.2.2. Style Comparison A second conventional method of performance evaluation called ‘‘style-comparison’’ involves comparison of return of a portfolio with that having a similar investment style. While there are many investment styles, one commonly used approach classifies investment styles as value versus growth. The ‘‘value style’’ portfolios invest in companies that are considered undervalued on the basis of yardsticks such as price-to-earnings and priceto-book value multiples. The ‘‘growth style’’ portfolios invest in companies whose revenue and earnings are expected to grow faster than those of the average company. In order to evaluate the performance of a valueoriented portfolio, one would compare the return on such a portfolio with that of a benchmark portfolio that has value-style. Similarly, a growthstyle portfolio is compared with a growth-style benchmark index. This method also suffers from the fact that while the style of the two portfolios that are compared may look similar, the risks of the two portfolios may be different. Also, the benchmarks chosen may not be truly comparable in terms of the style since there can be many important ways in which two similar style-oriented funds vary. Reilly and Norton (2003) provide an excellent disposition of the use of benchmark portfolios and portfolios style and the issues associated with their selection. Sharpe (1992), and Christopherson (1995) have developed methods for determining this style. 34.3. Risk-adjusted Methods The risk-adjusted methods make adjustments to returns in order to take account of the differences in risk levels between the managed portfolio and the benchmark portfolio. While there are many such methods, the most notables are the Sharpe ratio (S), Treynor ratio (T), Jensen’s alpha (a), Modigliani and Modigliani (M 2 ), and Treynor Squared (T 2 ). These measures, along with their applications, are discussed below. 34.3.1. Sharpe Ratio The Sharpe ratio (Sharpe, 1966) computes the risk premium of the investment portfolio per unit of total risk of the portfolio. The risk premium, also known as excess return, is the return of the portfolio less the risk-free rate of interest as measured by the yield of a Treasury security. The total risk is the standard deviation of returns of the portfolio. The numerator captures the reward for investing in a risky portfolio of assets in excess of the risk-free rate of interest while the denominator is the variability of returns of the portfolio. In this sense, the Sharpe measure is also called the ‘‘rewardto-variability’’ ratio. Equation (34.1) gives the Sharpe ratio: S¼ rp
rf sp (34:1) where S is the Sharpe ratio, rp the return of the portfolio, rf the risk-free rate, and sp the standard deviation of returns of the portfolio. The Sharpe ratio for an investment portfolio can be compared with the same for a benchmark portfolio such as the overall market portfolio. Suppose that a managed portfolio earned a return of PORTFOLIO PERFORMANCE EVALUATION 619 20 percent over a certain time period with a standard deviation of 32 percent. Also assume that during the same period the Treasury bill rate was 4 percent, and the overall stock market earned a return of 13 percent with a standard deviation of 20 percent. The managed portfolio’s risk premium is (20 percent
4 percent) ¼ 16 percent, while its Sharpe ratio, S, is equal to 16 percent=32 percent ¼ 0.50. The market portfolio’s excess return is (13 percent
4 percent) ¼ 9 percent, while its S equals 9 percent=20 percent ¼ 0.45. Accordingly, for each unit of standard deviation, the managed portfolio earned a risk premium of 0.50 percent, which is greater than that of the market portfolio of 0.45 percent, suggesting that the managed portfolio outperformed the market after adjusting for total risk. risk. In fact, in the above example, the portfolio earned an excess return of 16 percent whereas the market earned only 9 percent. These two numbers alone do not tell anything about the relative performance of the portfolio since the portfolio and the market have different levels of market risk. In this instance, the Treynor ratio for the managed portfolio equals (20 percent
4 percent)=1.5 ¼ 10.67, while that for the market equals (13 percent
4 percent)=1.00 ¼ 9.00. Thus, after adjusting for systematic risk, the managed portfolio earned an excess return of 10.67 percent for each unit of beta while the market portfolio earned an excess return of 9.00 percent for each unit of beta. Thus, the managed portfolio outperformed the market portfolio after adjusting for systematic risk. 34.3.2. Treynor Ratio 34.3.3. Jensen’s Alpha The Treynor ratio (Treynor, 1965) computes the risk premium per unit of systematic risk. The risk premium is defined as in the Sharpe measure. The difference in this method is in that it uses the systematic risk of the portfolio as the risk parameter. The systematic risk is that part of the total risk of an asset which cannot be eliminated through diversification. It is measured by the parameter known as ‘beta’ that represents the slope of the regression of the returns of the managed portfolio on the returns to the market portfolio. The Treynor ratio is given by the following equation: Jensen’s alpha (Jensen, 1968) is based on the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), and Mossin (1966). The alpha represents the amount by which the average return of the portfolio deviates from the expected return given by the CAPM. The CAPM specifies the expected return in terms of the risk-free rate, systematic risk, and the market risk premium. The alpha can be greater than, less than, or equal to zero. An alpha greater than zero suggests that the portfolio earned a rate of return in excess of the expected return of the portfolio. Jensen’s alpha is given by. T¼ rp
rf bp (34:2) where T is the Treynor ratio, rp the return of the portfolio, rf the risk-free rate, and bp the beta of the portfolio. Suppose that the beta of the managed portfolio in the previous example is 1.5. By definition, the beta of the market portfolio is equal to 1.0. This means the managed portfolio has one-and-half times more systematic risk than the market portfolio. We would expect the managed portfolio to earn more than the market because of its higher a ¼ rp
[rf þ bp (rm
rf )] (34:3) where a is the Jensen’s alpha, rp the return of the portfolio, rm the return of the market portfolio, rf the risk-free rate, and bp the beta of the portfolio. Using the same set of numbers from the previous example, the alpha of the managed portfolio and the market portfolio can be computed as follows. The expected return of the managed portfolio is 4 percent þ 1.5 (13 percent
4 percent) ¼ 17.5 percent. Therefore, the alpha of the managed