Risk, Return, & CAPM PDF

9/5/24 Return...

9/5/24 Return RETURN refers to “the total gain or loss experienced on an investment over a Risk, Return, & the Capital given period of time.” Asset Pricing Model (CAPM) presented by C.K.S. Almonte Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 214. Addison Wesley. 2 cont. Return cont. Return Formulae: Problem: Ending Value + Cash Flows You bought a share of JBX Corporation for HPR = Beginning Value PHP 20. A year later, you were able to sell HPY = HPR – 1 it for PHP 35 per share. Compute for its HPY. Annual HPY = Annual HPR – 1 where: Annual HPR = HPR1/n n = investment period (in years) Source: Reilly, F. K., & Brown, K. C. (2014). Analysis of investments and management of portfolios (10th ed., Philippine ed.), Chapter 1: An Overview of the Investment Process, Source (structure of the problem): Reilly, F. K., & Brown, K. C. (2014). Analysis of investments and management of portfolios (10th ed., Philippine ed.), Chapter 1: pp. 5-6. Cengage Learning Asia Pte Ltd. Note: (1) The HPR formula was modified by Almonte, C. K. S. (n.d.) to be consistent with Gitman (2003) (see: Gitman, L. J. (2003). An Overview of the Investment Process, pp. 5-6. Cengage Learning Asia Pte Ltd. Copyright 2014 by Cengage Learning Asia Pte Ltd. Note: Almonte, C.K.S. (March Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 214-216. Addison Wesley.) & (2) Almonte, C. K. S. (n.d.) did not use italics for the formulae. 3 29, 2022) mainly modified the values & currency. 4 cont. Return cont. Return Solution: Problem 2: You bought a share of JBX Corporation for PHP 35 + PHP 0 HPR = = 1.75 PHP 20. Three years later, you were able PHP 20 to sell it for PHP 45 per share. Determine its HPY & Annual HPY. HPY = 1.75 – 1 = 75% Source (structure of the problem): Reilly, F. K., & Brown, K. C. (2014). Analysis of investments and management of portfolios (10th ed., Philippine ed.), Chapter 1: An Overview of the Investment Process, pp. 5-6. Cengage Learning Asia Pte Ltd. Copyright 2014 by Cengage Learning Asia Pte Ltd. Note: Almonte, C.K.S. (March Solved by: Almonte, C.K.S. (March 29, 2022). 5 29, 2022) mainly modified the values & currency. 6 1  9/5/24 cont. Return Risk Solution: RISK refers to “the uncertainty that an investment will earn its expected rate of HPY = PHP 45 + PHP 0 −1= 2.25 −1= 125% return.” PHP 20 Annual HPY = Annual HPR – 1 = 2.251/3 – 1 = 1.310370697 – 1 Annual HPY = 31.04% Solved by: Almonte, C.K.S. (March 29, 2022). 7 Source: Reilly, F. K., & Brown, K. C. (2014). Analysis of investments and management of portfolios (10th ed., Philippine ed.), Chapter 1: An Overview of the Investment Process, p. 9. Cengage Learning Asia Pte Ltd 8 Accounting for Risk Risk Assessment: Range Risk may be ASSESSED &/or MEASURED. Formula: Risk ASSESSMENT – Sensitivity Analysis ~ Range Range = Optimistic Case − Pessimistic Case – Probability Distribution Risk MEASUREMENT – Standard Deviation (SD) – Coefficient of Variation (CV) Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 219-225. Addison Wesley. 9 Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 219. Addison Wesley. 10 Risk Measurement: SD Risk Measurement: CV Formulae: Formula: n σk = ∑ (k − k )2 * Pr j Note: The formulae j=1 j may be adapted to σk determine the CV = OR portfolio SD. k n ∑ (k j − k )2 σk = j=1 Use: k p & k p n −1 Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 222. Addison Wesley. Note: (1) Almonte, C. K. S. (n.d.) did not italicize the formulae & used an asterisk instead of a multiplication sign, (2) Almonte, C. K. S. (n.d.) corrected the Standard Deviation formulae with the “n-1’ (see: Gitman (2003, pp. 222, 226-227)). 11 Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 224. Addison Wesley. Note: Almonte, C. K. S. (n.d.) did not 12 italicize the formula. 2  9/5/24 Integrated Example: cont. Integrated Example: An Asset’s Risk An Asset’s Risk Determine each asset’s range, SD, & CV given Solutions: Range the following: Asset “C” Asset “D” RangeC = 10% − 2% = 8% Economic State Pr kC kD (in %) (in %) Decline 0.3 2 8 RangeD = 3% − 8% = 5% Stable 0.6 5 4 Upturn 0.1 10 3 Thus, asset “C” is riskier than asset “D”. Source (basic table format, required computation for each asset’s SD): Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, pp. 437-439 (Table 17-1). New York, NY. Printed in the United States of America. McGraw-Hill. Copyright 2012 by The McGraw-Hill Companies, Inc. Note: Almonte, C. K. S. (March 29, 2022) changed the given data / 13 Answered / Solved by: Almonte, C.K.S. (March 29, 2022, the format of the presentation & wording of the conclusion was updated on April 20, 2022). 14 values & modified the required computations for each asset. cont. Integrated Example: cont. Integrated Example: An Asset’s Risk An Asset’s Risk Solution: SDC Solution: SDD 2 2 2 2 kC k (k − k) C (k − k) C Pr (k − k) * Pr C kD k (k − k) D (k − k) D Pr (k − k) * Pr D 2% 4.6% (2.6%) 6.76% 0.3 2.028% 8% 5.1% 2.9% 8.41% 0.3 2.523% 5% 4.6% 0.4% 0.16% 0.6 0.096% 4% 5.1% (1.1%) 1.21% 0.6 0.726% 10% 4.6% 5.4% 29.16% 0.1 2.916% 3% 5.1% (2.1%) 4.41% 0.1 0.441% Total 5.040% Total 3.690% SDC = 5.040% = 2.24% SDD = 3.690% = 1.92% Note: The basic format of the Single-Asset’s SD table was adapted from Principles of managerial finance (10th ed.) (Chapter 5: Risk and Return) (p. 223) (Table 5.5), Note: The basic format of the Single Asset’s SD table was adapted from Principles of managerial finance (10th ed.) (Chapter 5: Risk and Return) (p. 223) (Table 5.5), by L. J. Gitman, 2003, United States. Addison Wesley. Copyright 2003 by Lawrence J. Gitman. by L. J. Gitman, 2003, United States. Addison Wesley. Copyright 2003 by Lawrence J. Gitman. Solved by: Almonte, C.K.S. (March 29, 2022). 15 Solved by: Almonte, C.K.S. (March 29, 2022). 16 cont. Integrated Example: cont. Integrated Example: An Asset’s Risk An Asset’s Risk Solution: SD Solution: CV Asset “C” Asset “D” SDC SDD SD 2.244994432% 1.920937271% 2.24% 1.92% Divide: k 4.6% 5.1% CV 0.49 0.38 Thus, asset “C” is riskier than asset “D”. Thus, asset “C” is riskier than asset “D”. Note: The basic format of the Single Asset’s CV table was adapted from Principles of managerial finance (10th ed.) (Chapter 5: Risk and Return) (p. 225), by L. J. Gitman, 2003, United States. Addison Wesley. Copyright 2003 by Lawrence J. Gitman. Answered / Solved by: Almonte, C.K.S. (March 29, 2022, the format of the presentation & wording of the conclusion was updated on April 20, 2022). 17 Answered / Solved by: Almonte, C.K.S. (March 29, 2022, the format of the presentation & wording of the conclusion was updated on April 20, 2022). 18 3  9/5/24 Example: cont. Example: A Portfolio’s Risk A Portfolio’s Risk Solve for the SDp given the following: Solution: SDp 2 Asset “C” Asset “D” kC kD kp kp (k p − kp ) (k p − kp 2 ) Pr (k p − kp ) * Pr 2% 8% 4.4% 4.8% (0.4%) 0.16% 0.3 0.048% Economic State Pr kC kD 5% 4% 4.6% 4.8% (0.2%) 0.04% 0.6 0.024% (in %) (in %) 10% 3% 7.2% 4.8% 2.4% 5.76% 0.1 0.576% Decline 0.3 2 8 Total 0.648% Stable 0.6 5 4 Upturn 0.1 10 3 Portfolio Mix 0.6 0.4 SDp = 0.648% = 0.80% Source (basic table format, required computation for the portfolio SD): Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., Note: The basic format of the Portfolio’s SD table was adapted from Principles of managerial finance (10th ed.) (Chapter 5: Risk and Return) (p. 223) (Table 5.5), by international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, pp. 437-442 (Table 17-1). New York, NY. Printed in the L. J. Gitman, 2003, United States. Addison Wesley. Copyright 2003 by Lawrence J. Gitman. United States of America. McGraw-Hill. Copyright 2012 by The McGraw-Hill Companies, Inc. Note: Almonte, C. K. S. (March 29, 2022) changed the given data / 19 Solved by: Almonte, C.K.S. (March 29, 2022). 20 values & “asked” to solve for the portfolio’s SD (related to Hirt & Block (2012)). cont. Example: Correlation Coefficient A Portfolio’s Risk Solution: Effect of Diversification: Formulae: Portfolio Asset “C” Asset “D” “C” = 60%, cov ij “D” = 40% rij = σk σ iσ j 2.24% 1.92% 0.80% Thus, diversification reduces risk. where: cov ij = ∑ k i − k i k j − k j P ( )( ) Source: Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, p. 460. McGraw-Hill. Note: Almonte, C. K. S. (March 31, 2022) did not italicize the formulae. Answered / Solved by: Almonte, C.K.S. (March 29, 2022, the format of the column heading “Portfolio... ” was updated on April 20, 2022). 21 22 Example: cont. Example: Correlation Coefficient Correlation Coefficient Find the correlation coefficient given the Solution: Correlation Coefficient following: kC kD (k ) (k )( ) P (k )( ) kC (k C − kC ) kD D − kD C − k C kD − kD C − k C kD − kD P Asset “C” Asset “D” 2% 4.6% (2.6%) 8% 5.1% 2.9% (7.54%) 0.3 (2.262%) 5% 4.6% 0.4% 4% 5.1% (1.1%) (0.44%) 0.6 (0.264%) Economic State Pr kC kD 10% 4.6% 5.4% 3% 5.1% (2.1%) (11.34%) 0.1 (1.134%) (in %) (in %) Total (3.660%) Decline 0.3 2 8 Stable 0.6 5 4 (3.660%) Upturn 0.1 10 3 rCD = = (0.85) 2.244994432% * 1.920937271% Portfolio Mix 0.6 0.4 Note: The basic format of the covariance table was adapted from Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, p. 460, by G. A. Hirt, & S. B. Block, 2012, New York, NY. McGraw-Hill. Copyright 2012 by The McGraw- Source (basic table format, required computation for the correlation coefficient): Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th Hill Companies, Inc. ed., international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, pp. 437-442, 460 (Table 17-1). New York, NY. Printed in the United States of America. McGraw-Hill. Copyright 2012 by The McGraw-Hill Companies, Inc. Note: (1) Almonte, C. K. S. (March 29, 2022) changed the given 23 Solved by: Almonte, C.K.S. (April 3, 2022, the format of the presentation & subscripts of the correlation coeeficient (r) were updated on April 21, 2022). 24 data / values, (2) Almonte, C. K. S. (March 31, 2022) “asked” to solve for the correlation coefficient (related to Hirt & Block (2012)). 4  9/5/24 Portfolio Theories CAPM Markowitz Portfolio Theory (MPT) Developed by SHARPE (1964), LINTNER Capital Asset Pricing Model (CAPM) (1965), & MOSSIN (1966) Arbitrage Pricing Theory (APT) The CAPM built on the MPT by taking into account the risk-free asset (RF).* Source: Reilly, F. K., & Brown, K. C. (2014). Analysis of investments and management of portfolios (10th ed., Philippine ed.), Chapter 8: An Source: Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Introduction to Asset Pricing Models, p. 205. Cengage Learning Asia Pte Ltd. Portfolio Management and Capital Market Theory, pp. 442-455, Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory: Appendix 17D: Arbitrage Pricing Theory, pp. 463-465. McGraw-Hill. 25 Source (with *): Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic 26 Look at Portfolio Management and Capital Market Theory, p. 446. McGraw-Hill. cont. CAPM cont. CAPM The CAPM ties the concepts of systematic Attributes of an EFFICIENT MARKET: risk & return of assets. The model: – A lot of investors with identical information & – Uses past data assumptions about securities – Presupposes EFFICIENT MARKETS – Free (from limitations with regards to investment, taxes, & transaction costs) – Sensible investors Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 235, 244. Addison Wesley. 27 Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 244. Addison Wesley. 28 cont. CAPM cont. CAPM Kinds of Risk: Formula: market risk premium – Nondiversifiable Risk or Systematic Risk or Market Risk or Beta Coefficient kj = RF + [ bj * (km – RF) ] – Diversifiable Risk or Unsystematic Risk risk premium Total Security Risk where: RF = k* + IP = Nondiversifiable Risk + Diversifiable Risk Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 234-235. Addison Wesley. 29 Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 238-239, 241. Addison Wesley. Note: (1) Almonte, C. K. S. (n.d.) did not italicize the formulae (kj & RF) & used an asterisk instead of a multiplication sign for kj. 30 5  9/5/24 cont. CAPM cont. CAPM Example: Solution: TUV Company gathered the following data kQ = 3% + [ 0.50 * (9% – 3%) ] relating to Asset Q: risk-free rate = 3%, kQ = 3% + 4.50% – 1.50% market return = 9%, & beta = 0.50. kQ = 6% Calculate the asset’s required return. Source (structure of the problem): Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 239. Addison Wesley. Copyright 2003 by Lawrence J. Gitman. Note: Almonte, C. K. S. (March 31, 2022) modified the problem by changing the firm name, asset name, & values. 31 Solved by: Almonte, C.K.S. (March 31, 2022). 32 cont. CAPM cont. CAPM A diagram of the CAPM is known as the Example: The SML: SECURITY MARKET LINE (SML). Variables Beta (in %) 0.0 0.5 1.0 1.5 2.0 Risk-free Rate 3 3 3 3 3 Market Return 9 9 9 9 9 Required Return 3 6 9 12 15 Note: The figure was adapted from Principles of corporate finance (10th ed., global ed.), by R. A. Brealey, S. C. Myers, & F. Allen, 2011, New York, NY. Printed in Singapore. McGraw-Hill/Irwin. Copyright 2011 by The McGraw-Hill Companies, Inc. (Source: Brealey, R. A., Myers, S. C., & Allen, F. (2011). Principles of corporate finance (10th ed., global ed.), Chapter 8: Portfolio Theory and the Capital Asset Pricing Model, p. 220 (Figure 8.6). McGraw-Hill/Irwin. Copyright Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, p. 240. Addison Wesley. 33 2011 by The McGraw-Hill Companies, Inc.) (Additional Note: Almonte, C. K. S. (March 31, 2022) modified the diagram. The screenshot was taken from Microsoft Excel for Mac 2011 Version 14.1.0 (110310)). 34 cont. CAPM cont. CAPM A change in INFLATION means a new A change in RISK-AVERSION means a required return. new required return. Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 241-242. Addison Wesley. 35 Source: Gitman, L. J. (2003). Principles of managerial finance (10th ed.), Chapter 5: Risk and Return, pp. 242-244. Addison Wesley. 36 6  9/5/24 cont. CAPM cont. CAPM CAPM Assumptions: cont. CAPM Assumptions: – Limitless funds may be obtained by investors – “All assets are perfectly divisible−it is possible – Investors use identical time horizons to buy fractional shares of any asset or – Investors assess investment opportunities by portfolio.” using the portfolio returns’ expected value & – Investments are free from taxes / transaction standard deviations costs – Investors project the same “probability – The market demonstrates efficiency distributions for rates of return.” Source: Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Source: Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, p. 453. McGraw-Hill. Portfolio Management and Capital Market Theory, p. 453. McGraw-Hill. 37 38 cont. CAPM cont. CAPM Some Critiques of the CAPM: Addressing Some of the Critiques of the CAPM: – Unclear proxy for RF Use portfolio beta (bp) instead of the individual security’s – Unclear km beta (bj) – Beta of individual securities may fluctuate as Formula: time goes by kp = RF + [ bp * (km – RF) ] Source: Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Source: Hirt, G. A., & Block, S. B. (2012). Fundamentals of investment management (10th ed., international student ed.), Chapter 17: A Basic Look at Portfolio Management and Capital Market Theory, p. 454. McGraw-Hill. Portfolio Management and Capital Market Theory, pp. 454-455. McGraw-Hill. 39 40 7