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1 TTh 3:15-4:30 Gates B01 Final Exam MS&E 247S Fri Aug PM-10PM Gates B01 (Official Time) Or Saturday Aug PM-10PM Gates B03 (Alternate Time) Remote SCPD participants will also take the exam on Friday, 8/14 Please Submit Exam Proctor s Name, Contact info as SCPD requires. C.c. the info to ffuy@stanford.edu, preferably three days before the exam. Local SCPD students please come to Stanford to take the exam. Light refreshments will be served. Handout #20 (as of Aug 11, 2009) International Asset Portfolios Equity Portfolios + Foreign Exchange Market Intervention

2 Wednesday office hours: 3 to 6 p.m. at Stanford Yang, Yamazaki 'green' building s Coffee House President John Hennessy spoke on March 5, 2008 at the dedication of the Jerry Yang & Akiko Yamazaki Environment and Energy Building. 15-2

3 Reading Assignments for this Week Scan Read Levich Chap 15 Pages Equity Portfolios + Chap 17 Foreign Exchange Market Intervention (pp ) Luenberger Chap Pages Solnik Eun 8, 9, 12, 13 Pages , , Alternate Investments, Int l Diversification, Performance Measurement, Global Asset Allocation: Structuring and Quantifying the Process Wooldridge Chap Chap Pages International Financial Management 4E:Chapter 13 International Equity Markets Pages 15-3

4 International Asset Portfolios Equity Portfolios MS&E 247S International Investments Yee-Tien Fu

5 Introduction to Equities While they share a long history, equities and bonds are very different financial instruments. The owner of a bond is entitled to a set amount of at periodic intervals. All bonds (excluding those with equity-like features) are claims on some nominal amount of. In comparison, the owner of an equity share in a British firm may receive dividends denominated in. But what the shareholder truly owns is a claim on the real assets of the firm and all the cash flows that accrue once the firm has paid all of its creditors. 15-5

6 Introduction to Equities Both bonds and shares may be exposed to similar market forces. If a bond was issued in London and trades in London, it will be subject to British exchange control risk, expropriation risks, and withholding taxes when viewed by non-british investors. The fundamental difference is this: The valuation of a bond is based on a stream of nominal cash flows that we can enumerate. The valuation of a British equity is linked to the firm s real assets (regardless of location) and the cash flows (in all currencies) associated with the firm s operations. 15-6

7 Introduction to Equities The performance of equity investments is usually evaluated in 2 dimensions - expected return and risk. These dimensions describe the 2 basic incentives for international investment: to enhance portfolio returns for the same level of risk, or to reduce the riskiness of a portfolio without sacrificing expected return. 15-7

8 Introduction to Equities Expected value gains could occur if foreign equity markets are inefficient, such that foreign equity prices do not reflect all available information, or if foreign equity markets may be segmented from other capital markets, such that investors in the foreign market receive a different compensation for bearing equity risk than in other markets. Diversification gains could occur if the correlation of returns across countries is low. 15-8

9 Introduction to Equities Diversification gains are available even when domestic and foreign capital markets are integrated, so that risk bearing in different markets is rewarded in a similar fashion. When investors are risk averse, international equity investment offers an opportunity for welfare gains through superior sharing of international equity risks. 15-9

10 Introduction to Equities A pioneering study by Herbert Grubel (1968) showed that investors from 11 developed economies could have enjoyed substantially more favorable risk-return opportunities had they diversified their portfolios internationally in the 1960s. However... The analysis overstated the gains. Capital restrictions would have made some markets off-limits to foreign investors.. The efficient frontier could not have been obtained by all investors

11 % Rate of Return (% per annum) Figure 15.1 Pg 524 Return and Risk in World Equity Markets and Efficient Frontiers, Efficient frontier labeled AA includes all 11 industrial countries, while BB includes only 8 European and North American countries Japan A A xx x x B x 2 Belgium Risk: Standard Deviation of Returns Australia x x B USA Canada France U.K. S. Africa Italy Germany Netherlands

12 Correlation Coefficient: Covariance of returns over the product of two standard deviation of returns 15-12

13 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

14 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

15 Introduction to Equities The portfolios in segment AA of the efficient frontier call for roughly a 40% weight on Australia. Since Australia represents less than 1% of the world equity market, these portfolios were inconsistent with the overall valuation of equity markets. Despite the shortcomings, Grubel s insight has been verified by many subsequent studies. Yet, despite promotion by investment advisors as a prudent strategy, most investor portfolios reflect a home country bias in equities as well as bonds, as shown in Table

16 Holdings of Foreign Securities by Residence of Investor Residence of investor US$ Value of Holdings (in billions) Equities % of Equity Portfolio Bonds % of Bond Portfolio Canada $ 9 $ 12 $ Germany Japan Netherlands U.K U.S Table

17 Introduction to Equities This investment pattern is a puzzle that has rekindled research into international equity markets. Have home country investors been inexcusably slow to diversify their portfolios internationally? Or have important aspects of the international investment process been left out of the theoretical and empirical analysis thus far? 15-17

18 Size and Institutional Features of Global Equity Markets Market Capitalization Measures From Figure 15.2, we see that U.S. market capitalization, while growing in absolute terms, has fallen in relative size from 54.1% of the world market in 1984 to 38.6% in Higher economic growth rates in smaller economies is the primary contributor to this long-term trend which is most likely to continue. Also note the substantial growth of emerging markets

19 World Market Capitalization US$ Trillions $ % 15.2% 19.4% 7.1% 54.1% $ % 18.2% 40.2% 7.9% 28.7% $ % 21.9% 21.3% 8.2% 37.0% $ % 24.6% 12.6% 8.1% 46.2% Figure 15.2 U.S. U.K. Japan Other Developed Emerging

20 Market Capitalization of Equity Markets in Developed Countries (in Billions of U.S. Dollars) 15-20

21 Market Capitalization of Equity Markets in Selected Developing Countries (in Billions of U.S. Dollars) 15-21

22 Size and Institutional Features of Global Equity Markets The pattern for Japan is unusual on 2 accounts: 1 Japan s share of world stock market capitalization more than doubled between 1984 and 1988, and then dropped by half in This reflects the surge in Japanese equity prices in the late 1980s, which many label a speculative bubble, and the collapse of those prices in The value of Japanese equities surpassed the U.S. in 1987 to become (for 3 years) the world s largest equity market. Note that the GNP of U.S. exceeds that of Japan by about 75%

23 How Large is the Japanese Stock Market? Cross-holding of securities (the practice of firm A owning equity shares in firm B) complicates the calculation of market capitalization values. Cross-holding is common in Japan, Germany, etc. where banks are permitted to hold substantial and sometimes controlling interests in non-banking firms. Cross-holding is fairly rare in the United States. Suppose firm A has $100 of net productive assets and 100 shares outstanding, each valued at $1. Firm B is similar. The market value of these 200 shares of firms A and B is $200. To introduce a cross-holding effect, let A issue 50 new shares at $1 each and use the proceeds to purchase shares in B

24 How Large is the Japanese Stock Market? As conventionally measured (taking the number of shares outstanding and multiplying by the price per share) the market value of firms A and B is now $250. Yet the value of productive physical assets is unchanged at $200, and $200 is sufficient to purchase all of A s and B s stock. It takes $150 to buy all of A s stock, and only $50 to buy the remaining shares of B not already acquired by purchasing A. Hence, to measure market value properly, we must adjust for the cross-holding effect by netting out the value of the cross-held shares. This adjustment reduced the 1988 market capitalization weight for Japan from 44% to 29.5%, a figure very close to Japan s GDP weight in the world portfolio

25 Size and Institutional Features of Global Equity Markets Institutional Aspects of Global Equity Markets Investors are unlikely to invest abroad if restrictions and limitations affect the repatriation of their capital. Number of Firms Listed In 1994, less than 7% of the firms listed on U.S. exchanges are foreign firms. In comparison, foreign firms make up about 18% of the total firms listed in United Kingdom, the center for trading in foreign stocks. The requirements for listing shares are more stringent in the U.S. than elsewhere

26 Size and Institutional Features of Global Equity Markets Market Concentration Market concentration, measured by the percentage of market capitalization within the 10 largest firms, is another statistic with wide variation across countries. In the U.S., Japan, and India, the top 10 firms account for 15-20% of the overall market capitalization. In all other countries, market concentration is higher, averaging close to 30%. In the Netherlands, New Zealand, and some smaller emerging markets, market concentration exceeds 60%

27 Percentage of Market Capitalization Represented by the 10 Largest Stocks: Emerging Equity Markets in Selected Developing Countries 15-27

28 Size and Institutional Features of Global Equity Markets Trading Volume Market turnover, measured as the annual volume of trading as a percentage of market capitalization, also varies substantially across countries. Statistics suggest that liquidity varies considerably across markets, as high trading volume tends to reduce liquidity risks and trading costs. But liquidity could vary as well within a market, with greater liquidity for a small number of high capitalization stocks, and much lower liquidity otherwise

29 Turnover Ratio of Equity Markets in Developed Countries (Transactions in US $ / Year-End Market Capitalization in US $) 15-29

30 Turnover Ratio of Emerging Equity Markets in Selected Developing Countries (Transactions in US $ / Year-End Market Capitalization in US $) 15-30

31 Size and Institutional Features of Global Equity Markets Transaction Taxes, Transaction Costs, Clearing and Settlement A long settlement period for making payment and obtaining delivery of securities (on the buy side) and delivering securities and obtaining cash settlement (on the sell side) is a deterrent to investment

32 15-32 Trading Practices and Costs of Major Equity Markets

33 Trading Practices and Costs of Major Equity Markets 15-33

34 International Investment Vehicles Direct Purchase of Foreign Shares American Depositary Receipts (ADRs) In order to issue an ADR, a U.S. bank takes custody of foreign shares in its foreign office. Then an ADR can be issued as a claim against these foreign shares. This can be especially valuable when there are doubts about the authenticity of foreign shares. Owners of the ADR have the right to redeem their ADR and obtain the true underlying foreign shares. Arbitrage of this sort ensures that the price of the ADR and the underlying shares will be nearly identical

35 Mechanics of Issuance and Cancellation of ADRs 15-35

36 International Investment Vehicles The issuing bank services the ADR by collecting all dividends, rights offerings, and so forth in foreign currency, and distributing the proceeds in US$ to the ADR owner. Rights offering - When a corporation is about to issue additional stock, it is customary to offer the stock first to its existing shareholders at special rate. U.S. investors can trade ADRs with each other without recourse to the foreign equity market, without using the foreign exchange market, and without relying on foreign clearing and settlement

37 Types of ADRs 15-37

38 International Investment Vehicles In a sponsored ADR, the foreign firm pays a fee to the depositary bank to cover the cost of the ADR program. In an unsponsored ADR, the issuance of the ADR is demand driven in response to a security firm s desire to facilitate trading in a popular foreign issue. Closed-End and Open-End Mutual Funds Mutual funds that invest in foreign stocks can be grouped into several categories - global, international, regional, country, specialty. In addition, foreign stock funds are classified as either open-end or closed-end

39 International Investment Vehicles An open-end fund stands ready to issue and redeem shares at prices reflecting the net-assetvalue of the underlying foreign shares. A closed-end fund issues a fixed number of shares against an initial capital offering. The shares of the fund then trade in a secondary market (usually listed on an exchange) at prices reflecting a premium or discount relative to the net-asset-value of the underlying foreign shares. Closed-end country funds were the fastest growing segment of the public investment funds during the late 1980s. At the end of 1992, there were 42 closed-end country funds listed in the U.S., representing $4.3 billion in equity

40 International Investment Vehicles 15-40

41 Global Depository Receipt Tombstone 15-41

42 Example of Dow Jones Country Stock Market Indexes 15-42

43 Major National Stock Market Indexes Major National Stock Market Indexes

44 International Investment Vehicles A 1994 paper by Gikas Hardouvelis, et al. analyzed the behavior of closed-end country fund discounts and premiums. They concluded that: Such discounts varied widely and are a significant factor in the variability of country fund returns. On average, the variance of country fund returns is 3 times larger than the variance on the underlying foreign assets. Discounts tend to be mean reverting, implying that unusually large discounts and premiums tend back toward their average value. Thus, by selecting a closed-end country fund, the investor also takes a position on an additional unobserved factor - the local sentiment about world events and country-specific events

45 Risk and Return in International Equity Markets Calculating the Unhedged Returns on Foreign Equity in US$ Terms Let E t represent the initial purchase price of the equity in foreign currency terms. Let S t represent the spot exchange rate, in $/FC terms, on the purchase date. The product E t S t is the US$ purchase price of the foreign equity. ~ After one period, the value of the equity is E t+1, representing the initial equity price plus the price change over the period ( ~ t+1 ) plus dividends D t+1 : ~ E t 1 E t ~ t 1 D t

46 Risk and Return in International Equity Markets The value of the equity after one period in US$ terms is ~ ~ E t+1 S t+1. The continuous rate of return on the foreign equity measured in US$ and on an unhedged basis is: E S E S R ~ ~ ~ ~ ~ t 1 t 1 t 1 t ~ ~ $, U ln ln ln 1 EFC S E S E S t t t US$,FC (15.1) The equation shows that the unhedged US$ return has 2 components: the return on the equity shares in foreign currency terms plus the return on the foreign currency used to buy the shares. Both terms may be greater than or less than zero. t 15-46

47 Risk and Return in International Equity Markets The variance of the returns reflects the variance of each term and the covariance between the returns on the foreign equity and the returns on spot foreign exchange: 2 ~ 2 ~ 2 ~ ~ ~ R E S 2Cov E ; S $, U FC US$,FC US$,FC (15.2) The covariance term represents the sensitivity of share returns to exchange rate changes, and can be either positive or negative. A positive covariance implies that the value of foreign equity tends to fall or rise along with the value of foreign currency as shown in cells A and B in Table FC 15-47

48 Currency Market Return and Stock Market Return Combinations Currency Market Return Negative Positive Stock Market Returns Negative Positive Stock Market Prices Spot FX (A) Stock Market Prices Spot FX (D) Stock Market Prices Spot FX (C) Stock Market Prices Spot FX (B) Table

49 Risk and Return in International Equity Markets The Mexican peso devaluation in late 1994 and early 1995 is an example of cell A, where capital flight and a loss in confidence in the Mexican economy brought the Mexican stock market down as well. With the peso overvalued and the country running a large current account deficit, Mexican policy makers allowed the peso to depreciate. Interest rates rose dramatically, as did import prices; the Mexican stock market dropped sharply in anticipation of a fall in Mexican GDP and corporate profits

50 $$ Pricing Determinants The analysis of international equity prices requires us to confront several challenging problems: 1 Are national equity markets integrated or segmented? 2 Are national equity markets efficient or inefficient? 3 Does purchasing power parity hold or not? 4 Do the assumptions of the capital asset pricing model (CAPM) apply or is arbitrage pricing theory (APT) more appropriate? 15-50

51 $$ Pricing Determinants The traditional CAPM hypothesizes that returns for an individual equity (R i ) in excess of the risk-free rate (R F ) are proportional to the systematic risk of the equity ( im ) times the expected market risk premium : R i R F im E R M R F where E(R M ) is the expected return on the market portfolio

52 $$ Pricing Determinants The assumptions of the traditional CAPM are: Investors maximize their utility which depends only on expected return (+) and risk (-). Investors have homogeneous expectations, agreeing about expected return and risk for all assets. Returns are expressed in nominal terms. A risk-free interest rate exists and unlimited borrowing and investing is possible at this rate. No transaction costs or taxes exist

53 $$ Pricing Determinants A security s is related to its covariance with the return on the market portfolio. regression coefficient iw 2 W tells us how much the security s rate of return tends to change when the return on the market portfolio changes. Thus, for a security with a of 2, if the market goes up by 10% more than what was expected, the return on the security will tend to go up by 20% more than what was expected

54 Definition of Risk When Investors Hold the Market Portfolio Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta ( )of the security. Beta measures the responsiveness of a security to movements in the market portfolio. i Cov( R 2 i, ( R R M M ) ) 15-54

55 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

56 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

57 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

58 $$ Pricing Determinants The CAPM leads to a separation, or mutual fund theorem, which claims that all investors will hold some combination of two assets: The risk-free asset and the market portfolio of all risky assets

59 15-59

60 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

61 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

62 Smart Risk-taking Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

63 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

64 Smart Risk-taking Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

65 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education. During the critical period of the financial crisis, Nikkei 225 and Don Jones demonstrated an usually high correlation coefficient of What might have caused it to happen? Was that because the international coordination of large-scaled stimulus programs? Was that partly due to the Japanese blue-chips omnipresent presence in the US? 15-65

66 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

67 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

68 Source: International Financial Management by Geert Bekaert; Robert J. Hodrick, 2008, Pearson Education

69 Is Investment in MNCs a Close Substitute for International Investment? If portfolios exhibit a home country bias, can investors argue that the shares of multinational corporations (MNCs) offer a close substitute for international diversification? The shares of an MNC could reflect real assets and/or cash flows from, say, 20 countries. So, the MNC could offer ready-made diversification and an inexpensive proxy for the purchase of 20 firms, each one based in a different country

70 Is Investment in MNCs a Close Substitute for International Investment? While this strategy sounds reasonable, the data reject the hypothesis that MNCs are a proxy for foreign markets or international diversification. A study by Jacquillat and Solnik (1978) examined the returns of MNCs from 9 countries by regressing their returns against all 9 market indexes. In each case, the returns on MNCs were most closely connected with the domestic market index. In the case of U.S. and U.K. MNCs, the addition of foreign markets offered virtually no improved explanation of MNC share returns

71 Policy Matters - Private Enterprises After 15 years, Let s ask the same question: Can investors create homemade international diversification? YES! Using data from 1973 to 1993 for seven developed and nine emerging markets, a study found that a set of domestically traded assets, including market indices, industry portfolios, 30 MNCs, closed-end country funds and ADRs, was successful at mimicking the gains from international portfolio diversification

72 Total, Domestic, and Foreign Company Listings on Major National Stock Exchanges for

73 Assignments from Chapter 15 Exercises 3, 4, 5. (no need to hand in) (Questions & answers are appended to this handout.) 15-73

74 Chap 17 Foreign Exchange Market Intervention (pp ) Overview Foreign Exchange Market Intervention Intervention as a Policy Instrument The Objectives of Central Bank Intervention The Mechanics of Intervention Empirical Evidence on Intervention The Effectiveness of Central Bank Intervention Security Transaction Taxes: Should We Throw Sand in the Gears of Financial Markets? 15-74

75 Foreign Exchange Market Intervention Many government actions (such as monetary policy, interest rate policy, fiscal spending, and taxation policies) can have an impact on the foreign exchange rate. The central bank may also intervene officially by directly purchasing or selling currency. Intervention is an essential part of a pegged exchange rate system

76 Foreign Exchange Market Intervention The modern experience of floating exchange rates is better described as a period of managed floating exchange rates. Note that acknowledging the importance of exchange rates and the potentially adverse effects of exchange rate misalignments or volatility does not automatically establish a valid case for central bank intervention

77 Foreign Exchange Market Intervention Under floating exchange rates, an active intervention policy presumes that: markets are at times inefficient, thus permitting misaligned or excessively volatile rates, policymakers can identify such market inefficiencies, intervention techniques can correct the misalignments and excess volatility, and the benefits from the correction exceed the costs of conducting the intervention

78 The Objectives of Central Bank Intervention Shortly after the breakdown of the Bretton Woods Agreement in 1973, the International Monetary Fund (IMF) enacted a set of guidelines designed to limit the use of intervention and the potential for conflicts among nations

79 The Objectives of Central Bank Intervention The guidelines, which are still in effect, specify that member nations of the IMF: Have an obligation to intervene to prevent disorderly conditions in the foreign exchange market. Should avoid manipulating exchange rates to prevent balance of payments adjustment or gain an unfair competitive advantage in trade. Should take into account the interests and policies of other members when setting their own intervention policies

80 Eun: International Financial Management Chapter 4: The Market for Foreign Exchange

81 Eun: International Financial Management Chapter 4: The Market for Foreign Exchange

82 Stephen G. Cecchetti on Central Banks, Monetary Policy, and Financial Stability (great optional reading) Chapter 15 Central Banks in the World Today 2_ch15.pdf 15-82

83 Stephen G. Cecchetti on Central Banks, Monetary Policy, and Financial Stability (great optional reading) Chapter 16 The Structure of Central Banks: The Federal Reserve and the European Central Bank 2_ch16.pdf 15-83

84 The Mechanics of Intervention Central bank interventions typically occur in the spot foreign exchange market. If the domestic currency is stronger than desired, the central bank sells domestic currency, and vice versa. Central bank interventions may generate direct effects associated with the changed quantities of money and/or bonds. The magnitude of the effects depends on whether the intervention was sterilized or unsterilized

85 The Mechanics of Intervention An unsterilized intervention is simply a foreign exchange market sale or purchase. The money supplies in both countries are affected. A sterilized intervention includes an offsetting transaction in the domestic money market (such as the purchase or sale of government securities) that reverses, or sterilizes, the impact of the initial intervention transaction. The money supplies remain unchanged, but the bond supplies are affected

86 The Mechanics of Intervention According to the monetary approach, sterilized interventions have no direct impact on the exchange rate. However, according to the portfolio balance approach, the relative supply of government bonds helps to determine the exchange rate

87 The Mechanics of Intervention Central bank interventions may also generate indirect effects: They may signal the market about future monetary and fiscal policies. They may interrupt short-term patterns in rates and reduce the profitability and incidence of noise trading

88 Empirical Evidence on Intervention From 1982 to 1991, the U.S. Federal Reserve sold $35.8 billions and purchased $15.8 billions. Note that the interventions were small compared with the daily foreign exchange trading volume. There was also evidence of coordinated interventions with other central banks, such as the German Bundesbank and the Swiss National Bank

89 The Effectiveness of Central Bank Intervention Does intervention have any effect - beneficial or detrimental - on the course of exchange rates and the ability of policymakers to achieve their larger macroeconomic goals? The debate hinges on whether a market failure has occurred and whether official intervention can correct this failure

90 The Effectiveness of Central Bank Intervention Private Speculation Official Intervention A C Stabilizing Efficient markets view Official intervention smoothes the market Credible signals of future policy remove uncertainty Encourages stabilizing private speculators B D Destabilizing Inefficient markets: Stabilization policy gamed bandwagons, bubbles, by market and becomes noise traders destabilizing Intervention is inconsistent with underlying economic policies 15-90

91 The Effectiveness of Central Bank Intervention Evidence suggests that intervention may stabilize exchange rates by lowering the daily volatility, as well as cause the rates to move in the intended direction. It seems that interventions send the strongest signals and have the highest chance of success when the conditions of surprise, publicity, and coordination with other central banks, are met

92 Assignments from Chapter 17 Exercises 1, 2, 3, 4. (no need to hand in) (Questions & answers are appended to this handout.) 15-92

93 Excel Finance Gallery Available at Companion Website for Oxford Handbook of Financial Modeling by Ho and Lee Oup.org (Oxford University Press Website) 94 downloadable Excel Templates for Finance Modelers

94 Ross / Corporate Finance 7E / CAPM Capital Asset Pricing Model 10.3 The Return and Risk for Portfolios Stock fund Bond Fund Rate of Squared Rate of Squared Scenario Return Deviation Return Deviation Recession -7% 3.24% 17% 1.00% Normal 12% 0.01% 7% 0.00% Boom 28% 2.89% -3% 1.00% Expected return 11.00% 7.00% Variance Standard Deviation 14.3% 8.2% Note that stocks have a higher expected return than bonds and higher risk. Let us turn now to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks

95 10.3 The Return and Risk for Portfolios Rate of Return Scenario Stock fund Bond fund Portfolio squared deviation Recession -7% 17% 5.0% 0.160% Normal 12% 7% 9.5% 0.003% Boom 28% -3% 12.5% 0.123% Expected return 11.00% 7.00% 9.0% Variance Standard Deviation 14.31% 8.16% 3.08% The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: r P w B r B w 5% 50% ( 7%) 50% (17%) S r S 15-95

96 10.3 The Return and Risk for Portfolios Rate of Return Scenario Stock fund Bond fund Portfolio squared deviation Recession -7% 17% 5.0% 0.160% Normal 12% 7% 9.5% 0.003% Boom 28% -3% 12.5% 0.123% Expected return 11.00% 7.00% 9.0% Variance Standard Deviation 14.31% 8.16% 3.08% The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio: r P w B r B w S r S 12.5% 50% (28%) 50% ( 3%) 15-96

97 10.3 The Return and Risk for Portfolios Rate of Return Scenario Stock fund Bond fund Portfolio squared deviation Recession -7% 17% 5.0% 0.160% Normal 12% 7% 9.5% 0.003% Boom 28% -3% 12.5% 0.123% Expected return 11.00% 7.00% 9.0% Variance Standard Deviation 14.31% 8.16% 3.08% The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio. E( r ) P wb E( rb ) ws E( rs 9 % 50% (11%) 50% (7%) ) 15-97

98 10.3 The Return and Risk for Portfolios Rate of Return Scenario Stock fund Bond fund Portfolio squared deviation Recession -7% 17% 5.0% 0.160% Normal 12% 7% 9.5% 0.003% Boom 28% -3% 12.5% 0.123% Expected return 11.00% 7.00% 9.0% Variance Standard Deviation 14.31% 8.16% 3.08% The variance of the rate of return on the two risky assets portfolio is σ P (wbσ B ) (wsσ S ) 2(wBσ B )(wsσ S )ρ BS where BS is the correlation coefficient between the returns on the stock and bond funds

99 10.3 The Return and Risk for Portfolios Rate of Return Scenario Stock fund Bond fund Portfolio squared deviation Recession -7% 17% 5.0% 0.160% Normal 12% 7% 9.5% 0.003% Boom 28% -3% 12.5% 0.123% Expected return 11.00% 7.00% 9.0% Variance Standard Deviation 14.31% 8.16% 3.08% Observe the decrease in risk that diversification offers. An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than stocks or bonds held in isolation

100 10.4 The Efficient Set for Two Assets % in stocks Risk Return 0% 8.2% 7.0% 5% 7.0% 7.2% 10% 5.9% 7.4% 15% 4.8% 7.6% 20% 3.7% 7.8% 25% 2.6% 8.0% 30% 1.4% 8.2% 35% 0.4% 8.4% 40% 0.9% 8.6% 45% 2.0% 8.8% 50.00% 3.08% 9.00% 55% 4.2% 9.2% 60% 5.3% 9.4% 65% 6.4% 9.6% 70% 7.6% 9.8% 75% 8.7% 10.0% 80% 9.8% 10.2% 85% 10.9% 10.4% 90% 12.1% 10.6% 95% 13.2% 10.8% 100% 14.3% 11.0% P o rtfo lio R e turn 12.0% 11.0% 10.0% 9.0% 8.0% 7.0% 6.0% 5.0% Portfolo Risk and Return Combinations 100% bonds 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% Portfolio Risk (standard deviation) We can consider other portfolio weights besides 50% in stocks and 50% in bonds 100% stocks

101 10.4 The Efficient Set for Two Assets % in stocks Risk Return 0% 8.2% 7.0% 5% 7.0% 7.2% 10% 5.9% 7.4% 15% 4.8% 7.6% 20% 3.7% 7.8% 25% 2.6% 8.0% 30% 1.4% 8.2% 35% 0.4% 8.4% 40% 0.9% 8.6% 45% 2.0% 8.8% 50% 3.1% 9.0% 55% 4.2% 9.2% 60% 5.3% 9.4% 65% 6.4% 9.6% 70% 7.6% 9.8% 75% 8.7% 10.0% 80% 9.8% 10.2% 85% 10.9% 10.4% 90% 12.1% 10.6% 95% 13.2% 10.8% 100% 14.3% 11.0% P o rtfo lio R e turn 12.0% 11.0% 10.0% 9.0% 8.0% 7.0% 6.0% 5.0% Portfolo Risk and Return Combinations 100% bonds 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% Portfolio Risk (standard deviation) We can consider other portfolio weights besides 50% in stocks and 50% in bonds 100% stocks

102 10.4 The Efficient Set for Two Assets % in stocks Risk Return 0% 8.2% 7.0% 5% 7.0% 7.2% 10% 5.9% 7.4% 15% 4.8% 7.6% 20% 3.7% 7.8% 25% 2.6% 8.0% 30% 1.4% 8.2% 35% 0.4% 8.4% 40% 0.9% 8.6% 45% 2.0% 8.8% 50% 3.1% 9.0% 55% 4.2% 9.2% 60% 5.3% 9.4% 65% 6.4% 9.6% 70% 7.6% 9.8% 75% 8.7% 10.0% 80% 9.8% 10.2% 85% 10.9% 10.4% 90% 12.1% 10.6% 95% 13.2% 10.8% 100% 14.3% 11.0% P ortfolio R eturn 12.0% 11.0% 10.0% 9.0% 8.0% 7.0% 6.0% 5.0% Portfolo Risk and Return Combinations 100% bonds 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% Portfolio Risk (standard deviation) 100% stocks Note that some portfolios are better than others. They have higher returns for the same level of risk or less. These compromise the efficient frontier

103 Definition of Risk When Investors Hold the Market Portfolio Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta ( )of the security. Beta measures the responsiveness of a security to movements in the market portfolio. i Cov( R 2 i, ( R R M M ) )

104 Estimating with regression Characteristic Characteristic Line Line Slope = i Security Returns Security Returns Return on market % R i = i + i R m + e i

105 Estimates of for Selected Stocks Stock Bank of America Borland International Travelers, Inc. Du Pont Kimberly-Clark Corp. Microsoft Green Mountain Power Beta Homestake Mining Oracle, Inc

106 The Formula for Beta i Cov( R 2 i, ( R R M M ) ) Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio

107 10.9 Relationship between Risk and Expected Return (CAPM) Expected Return on the Market: R M R F Market Risk Premium Expected return on an individual security: R i R F β i ( R M R F ) Market Risk Premium This applies to individual securities held within welldiversified portfolios

108 Expected Return on an Individual Security This formula is called the Capital Asset Pricing Model (CAPM) R i R F β i ( R M R F ) Expected return on a security = Riskfree rate + Beta of the security Market risk premium Assume i = 0, then the expected return is R F. Assume i = 1, then Ri RM

109 Relationship Between Risk & Expected Return Expected return R M R i R F β i ( R M R F ) R F

110 Relationship Between Risk & Expected Return Expected return 13.5% 3% β 1.5 3% 1.5 i R F RM 10% Ri 3% 1.5 (10% 3%) 13.5%

111 10.10 Summary and Conclusions This chapter sets forth the principles of modern portfolio theory. The expected return and variance on a portfolio of two securities A and B are given by E( r ) P wa E( ra ) wb E( rb ) σ P (waσ A ) (wbσ B ) 2(wσ B B )(wσ A A )ρ AB By varying w A, one can trace out the efficient set of portfolios. We graphed the efficient set for the two-asset case as a curve, pointing out that the degree of curvature reflects the diversification effect: the lower the correlation between the two securities, the greater the diversification. The same general shape holds in a world of many assets

112 10.10 Summary and Conclusions The efficient set of risky assets can be combined with riskless borrowing and lending. In this case, a rational investor will always choose to hold the portfolio of risky securities represented by the market portfolio. Then with borrowing or lending, the investor selects a point along the CML. return M CML efficient frontier r f P

113 10.10 Summary and Conclusions The contribution of a security to the risk of a well-diversified portfolio is proportional to the covariance of the security's return with the market s return. This contribution is called the beta. Cov( Ri, RM i 2 ( R ) The CAPM states that the expected return on a security is positively related to the security s beta: M ) R i R F β i ( R M R F )

114 Ross / Corporate Finance 7E / CAPM 12.1 The Cost of Equity Capital Firm with excess cash Pay cash dividend A firm with excess cash can either pay a dividend or make a capital investment Shareholder invests in financial asset Invest in project Shareholder s Terminal Value Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk

115 The Cost of Equity From the firm s perspective, the expected return is the Cost of Equity Capital: R i R F β R i ( M RF ) To estimate a firm s cost of equity capital, we need to know three things: 1. The risk-free rate, R F 2. The market risk premium, 3. The company beta, β i RM R F Cov( R i, Var( R R M M ) ) σ σ i, M 2 M

116 Example Suppose the stock of Stansfield Enterprises, a publisher of PowerPoint presentations, has a beta of 2.5. The firm is 100-percent equity financed. Assume a risk-free rate of 5-percent and a market risk premium of 10-percent. What is the appropriate discount rate for an expansion of this firm? R R R F β i ( R M R ) F 5 % % R 30%

117 Example (continued) Suppose Stansfield Enterprises is evaluating the following nonmutually exclusive projects. Each costs $100 and lasts one year. Project Project Project s Estimated Cash Flows Next Year IRR NPV at 30% A 2.5 $150 50% $15.38 B 2.5 $130 30% $0 C 2.5 $110 10% -$

118 Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects Project IRR Good project A SML 30% B 5% C 2.5 Bad project Firm s risk (beta) An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall short of the cost of capital

119 12.2 Estimation of Beta: Measuring Market Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock s return to the return on the market portfolio

120 12.2 Estimation of Beta Theoretically, the calculation of beta is straightforward: β Cov( Ri, R Var( R ) M M Problems 1. Betas may vary over time. 2. The sample size may be inadequate. 3. Betas are influenced by changing financial leverage and business risk. Solutions Problems 1 and 2 (above) can be moderated by more sophisticated statistical techniques. Problem 3 can be lessened by adjusting for changes in business and financial risk. Look at average beta estimates of comparable firms in the industry. M ) σ σ i, M

121 Stability of Beta Most analysts argue that betas are generally stable for firms remaining in the same industry. That s not to say that a firm s beta can t change. Changes in product line Changes in technology Deregulation Changes in financial leverage

122 Using an Industry Beta It is frequently argued that one can better estimate a firm s beta by involving the whole industry. If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta. If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm s beta. Don t forget about adjustments for financial leverage

123 Modern Financial Markets: Prices, Yields, and Risk Analysis Blackwell, Griffiths and Winters Chapter 15 Stock Portfolio Formation and Risk Management

124 Learning Objectives 1. Portfolio formation and correlation 2. Measuring portfolio risk 3. Incremental value-at-risk 4. Portfolio risk management strategies using derivative securities

125 The Basics of Portfolio Formation A portfolio is a group of assets. The relative importance (weight) of an asset in a portfolio is based on the asset s contribution to the value of the portfolio. We will focus on forming a stock portfolio

126 The Basics of Portfolio Formation (cont.) Example Let s assume we have 15,000 invested in our portfolio and the investment is divided among three stocks: FLYBY 5,000 33% UO 6,000 40% GDAY 4,000 27%

127 The Basics of Portfolio Formation (cont.) Example (cont.) Investment Expected Return (Annual) Standard Deviation (Monthly) Beta FLYBY 11% 10% 1.05 UO 9% 5% 0.95 GDAY 12% 7% 1.11 Correlation Coefficients FLYBY UO GDAY FLYBY UO GDAY

128 The Basics of Portfolio Formation (cont.) Example (cont.) So, what is the likely return on the portfolio? The answer is the weighted average of the individual returns. E[R] = w1*r1 + w2 * r2 + w3*r3 = 0.33(11%) (9%) (12%) = 10.47% Also, what is the Beta (β) of the portfolio? The answer is the weighted average of the individual Betas. E[β] = w1*β1 + w2 *β2 + w3*β3 = 0.33(1.05) (0.95) (1.11) =

129 The Basics of Portfolio Formation (cont.) Example (cont.) The third calculation we would like to do for our portfolio is its standard deviation. However, the standard deviation of the portfolio is not the weighted average of the individual standard deviations because of the difference between diversifiable and non-diversifiable risk

130 The Basics of Portfolio Formation (cont.) Correlation The degree of correlation is a measure of the extent to which returns on two assets move together. If both move up and down together, they are positively correlated and ρ ij >

131 Return Return The Basics of Portfolio Formation (cont.) Correlation (cont.) Perfect Positive Correlation Stock A Less Than Perfect Positive Correlation Time Stock B Time Stock A Stock B

132 Return Return The Basics of Portfolio Formation (cont.) Correlation (cont.) If one moves up when the other moves down, they are negatively correlated and ρ ij < 0. Perfect Negative Correlation Stock B Less Than Perfect Negative Correlation Stock B Stock A Stock A Time Time

133 Return The Basics of Portfolio Formation (cont.) Correlation (cont.) If the two assets are completely independent, then they are uncorrelated and ρ ij = 0. Zero Correlation Stock B Time Stock A

134 Measuring Portfolio Risk We now want to measure portfolio risk and since a portfolio has more than one asset we have to consider the correlation of the assets in the portfolio. The standard deviation of a portfolio includes the correlation between the assets in the portfolio and thus provides a measure of portfolio risk

135 Measuring Portfolio Risk (cont.) The formula for portfolio standard deviation is: p 2 2 w 2 w w 0. 5 i i i j ij i j

136 Measuring Portfolio Risk (cont.) Now, let s return to our portfolio and calculate its standard deviation. INVESTMENT FLYBY UO GDAY FLYBY UO GDAY The shaded area (on the diagonal) represent the weighted total risk of the of the individual securities in the portfolio, which in the formula is Σw i2 σ 2 i

137 Measuring Portfolio Risk (cont.) The off-diagonal items represent the correlations between the different assets in the portfolio and the formula is: 2(ΣΣw i w j ρ ij σ i σ j ) The formula starts by multiplying by 2 because the items above the diagonal are the same as the items below the diagonal

138 Measuring Portfolio Risk (cont.) Using our portfolio, the cells of the figure are as follows: INVESTMENT FLYBY UO GDAY FLYBY (0.33) 2 (.1) 2 (.33)(.4)(.8)(.1)(.05) (.33)(.27)(.5)(.1)(.07) UO (0.4) 2 (0.05) 2 (.4)(.27)(.2)(.05)(.07) GDAY (0.27) 2 (.07)

139 Measuring Portfolio Risk (cont.) Now, the calculation for the portfolio standard deviation is: p p 2 wi [(.33) 2 2 i (.1) 2 2 (.4) 2 w w i (.05) 2 j ij i j (.27) (.07) 2((.33)(.4)(.8)(.1)(.05) (.33)(.27)(.5)(.1)(.07) (.4)(.27)(.2)(.05)(.07))] [ ( )] 0.5 [ ] or 6.06%

140 Measuring Portfolio Risk (cont.) The financial definition of risk is uncertainty and standard deviation provides a measure of uncertainty. However, individuals often think of risk in terms of losses and focus on the absolute dollar value of their losses. The focus on dollar losses as a concept of risk has led to the development of an alternative measure of risk called Value-at- Risk

141 Value-at-Risk To measure value-at-risk, we change our focus from portfolio percentages to dollar value invested. With this change we can measure portfolio standard deviation in terms of dollar value invested. That is, we replace the portfolio percentage weights with the dollar values invested. The calculation for our portfolio is as follows:

142 Value-at-Risk (cont.) p p Continuing with our portfolio, the portfolio standard deviation based on value invested is. 2 wi [(5000) 2 i 2 2 (.1) 2 (6000) w w i 2 j ij (.05) i 2 j 0.5 (4000) 2 (.07) 2((5000)(6000)(.8)(.1)(.05) (5000)(4000)(.5)(.1)(.07) (6000)(4000)(.2)(.05)(.07))] [250,000 90,000 78,400 2(120,000 70,000 16,800)] 0.5 [832,000]

143 Value-at-Risk (cont.) Having calculated the portfolio standard deviation in terms of value invested, we have completed the first step in determining Valueat-Risk. Value-at-Risk provides the expected maximum loss over a target horizon with a given level of confidence

144 Value-at-Risk (cont.) To calculate Value-at-Risk, we need two more pieces of information: 1. Length of holding period, which is chosen to match the amount of time required to liquidate the portfolio in an orderly manner. 2. Confidence interval, which is a function of the amount of risk aversion of the investor. Higher confidence intervals imply higher value-at-risk figures

145 Value-at-Risk (cont.) Both measures are somewhat arbitrary and are chosen to fit the situation and the investors. For a stock portfolio, a common horizon is one month and we will choose a confidence level of 5% for our calculation of value-at-risk

146 Value-at-Risk (cont.) Recall from statistics that the point estimate from a confidence level is as follows: Point estimate = +/- (confidence level critical value) * (standard deviation) Since we are looking at value losses, we focus only on the left tail of the distribution

147 Value-at-Risk (cont.) Assuming that the changes in the value of our portfolio are normally distributed then the critical value for the confidence interval can been seen from Figure N(d) c = 5% confidence level d = Standard Normal Variable

148 Value-at-Risk (cont.) Value-at-Risk calculation: Portfolio standard deviation in value is and critical value for 5% lower tail confidence interval is So, the value-at-risk is 1, = ( *1.65). This means that we are 95% confident that our maximum monthly loss is 1,

149 Incremental Value-at-Risk Value-at-Risk provides a calculation of portfolio risk. However, we may want to know which security provides the most risk (or threat to maintaining value) in our portfolio. We can address this question by calculating incremental value-at-risk

150 Incremental Value-at-Risk (cont.) Incremental value-at-risk is a two step calculation with the steps as follows: 1. Calculate the individual stock value variance in the portfolio followed by 2. Calculating the individual stock contribution to the value-at-risk for the portfolio

151 Incremental Value-at-Risk (cont.) Step 1 of incremental value-at-risk Stock Positio n Variance + Position Covariance + Position Covariance FLYBY 5, , , = UO 6, , , = GDAY 4, , , = Recall that covariance = ρ ij σ i σ j so the covariance between GDAY and FLYBY is (0.5)(.1)(.07) =

152 Incremental Value-at-Risk (cont.) Step 2 of incremental value-at-risk Stock Stock (Variance/ Covariance) Portfolio Variance * Portfolio Value-at- Risk * Stock Wealth Position FLYBY * * 5,000 = UO * * 6,000 = GDAY * * 4,000 = Total (rounded)

153 Incremental Value-at-Risk (cont.) Points from incremental value-at-risk. 1. FLYBY puts the most value-at-risk even though at is not the largest investment in the portfolio. 2. UO has the lowest value variance (from Step 1) but is not the least risky portion of our portfolio because of the large value investment in UO