ECON 372: Business Finance 2 Risk and Return in Capital Markets (part 1) Copyright © 2020 Pearson Canada Inc. 3-1 Learning Objectives • Identify which types of securities have historically had the highest returns and which have been the most volatile • Compute the average return and volatility of returns from a set of historical asset prices • Understand the tradeoff between risk and return for large portfolios versus individual stocks Copyright © 2020 Pearson Canada Inc. 3-2 10.1 A First Look at Risk and Return • Consider how an investment would have grown if it were invested in each of the following from the end of 1956 until the beginning of 2014: – – – – S&P/TSX Composite Index: 9.3% Standard & Poor’s 500 (S&P 500) – avg return: 9.5% Long-term Government of Canada bonds: Government of Canada Treasury Bills – smallest return Copyright © 2020 Pearson Canada Inc. 3-3 10.2 Historical Risks and Returns of Stocks • Computing Historical Returns – Realized Returns – Individual Investment Realized Returns βͺ The realized return from your investment in the stock from t to t + 1 is: π·ππ£π‘+1 + ππ‘+1 − ππ‘ π·ππ£π‘+1 ππ‘+1 − ππ‘ = + ππ‘ ππ‘ ππ‘ = π·ππ£πππππ πππππ + πΆππππ‘ππ πΊπππ πππππ π π‘+1 = Copyright © 2020 Pearson Canada Inc. (Eq. 10.1) 3-4 Example 10.1: Realized Return • Barrick Gold Corp. stock (ticker symbol: ABX.TO) paid a dividend of $0.03 on February 24, 2017. (Note: Barrick pays dividends in U.S. dollars [USD], but Canadian financial websites such as Yahoo!Finance Canada (ca.finance.yahoo.com ) report the dividends in Canadian dollars [CAD] when one uses Barrick’s Toronto Stock Exchange ticker symbol ABX.TO instead of the New York Stock Exchange symbol ABX.) Suppose you bought Barrick stock for $21.49 on December 30, 2016 and sold it immediately after the dividend was paid for $25.59. What was your realized return from holding the stock? Copyright © 2020 Pearson Canada Inc. 3-5 Example 10.1: Realized Return: Plan • We can use Equation 10.1 to calculate the realized return. Knowing the purchase price ($21.49), the selling price ($25.59), and the dividend ($0.03), we are ready to proceed. Copyright © 2020 Pearson Canada Inc. 3-6 Example 10.1: Realized Return: Execute • Using Equation 10.1, the return from December 30, 2016, until February 24, 2017, is equal to: Divt +1 + Pt +1 − Pt 0.03 + 25.59 − 21.49 Rt +1 = = = 0.192, or19.2% Pt 21.49 • This 19.2% can be broken down into the dividend yield and the capital gain yield: DivYield = Divt + 1 Pt 0.03 = = 0.001, or 0.1% 21.49 Pt +1 − Pt (25.59 − 21.49) Capital Gain Yield = = = 0.191, or 19.1% Pt 21.49 Copyright © 2020 Pearson Canada Inc. 3-7 Example 10.1: Realized Return: Evaluate These returns include both the capital gain and the return generated from receiving dividends. Both dividends and capital gains contribute to the total realized return—ignoring either one would give a very misleading impression of Barrick’s performance. Copyright © 2020 Pearson Canada Inc. 3-8 10.2 Historical Risks and Returns of Stocks • Computing Historical Returns – Individual Investment Realized Returns βͺ For quarterly returns (or any four compounding periods that make up an entire year) the annual realized return, Rannual, is found by compounding: 1 + Rannual = (1 + R1 )(1 + R2 )(1 + R3 )(1 + R4 ) Copyright © 2020 Pearson Canada Inc. (Eq.10.2) 3-9 Example 10.2: Compounding Realized Returns • Suppose you purchased Barrick Gold Corp. stock (ticker symbol: ABX.TO) on December 30, 2016, and held it for one year, selling on January 2, 2018. What was your realized return? Copyright © 2020 Pearson Canada Inc. 3 - 10 Example 10.2: Compounding Realized Returns: Plan (2 of 2) • We need to analyze the cash flows from holding ABX stock for each quarter. In order to obtain the cash flows, we must look up ABX stock price data at the start and end of both years, as well as at any dividend dates (see Chapter 7 and the textbook’s website for online sources of stock price and dividend data). From the data, we can construct the following table to fill out our cash flow timeline: Copyright © 2020 Pearson Canada Inc. 3 - 11 Example 10.2: Compounding Realized Returns: Plan (1 of 2) Date Price ($) Dividend ($) 30-Dec-16 $21.49 24-Feb-17 $25.59 $0.03 29-May-17 $22.07 $0.03 29-Aug-17 $22.27 $0.03 29-Nov-17 $18.05 $0.03 02-Jan-18 $19.01 Source: Barrick Gold Corp. and Yahoo!Finance Canada. Next, compute the return between each set of dates using Equation 10.1. Then determine each annual return in a way similar to that shown in Equation 10.2 by compounding the returns for all of the periods in that year. Copyright © 2020 Pearson Canada Inc. 3 - 12 Example 10.2: Compounding Realized Returns: Execute (1 of 3) • In Example 10.1, we already computed the realized return for December 30, 2016, to February 24, 2017, as 19.2%. We continue as in that example, using Equation 10.1 for each period until we have a series of realized returns. For example, from August 29, 2017, to November 29, 2017, the realized return is: Rt +1 = Divt + 1 + Pt +1 − Pt Pt 0.03 + (18.05 − 22.27) = = − 0.188, or − 18.8% 22.27 Copyright © 2020 Pearson Canada Inc. 3 - 13 Example 10.2: Compounding Realized Returns: Execute (2 of 3) The table below includes the realized return in each period. Date Price ($) Dividend ($) Return 30-Dec-16 $21.49 24-Feb-17 $25.59 $0.03 19.2% 29-May-17 $22.07 $0.03 −13.6% 29-Aug-17 $22.27 $0.03 1.0% 29-Nov-17 $18.05 $0.03 −18.8% 02-Jan-18 $19.01 Annual Return over 2017: Copyright © 2020 Pearson Canada Inc. 5.3% −11.0% 3 - 14 Example 10.2: Compounding Realized Returns: Execute (3 of 3) • We then determine the one-year return by compounding. 1 + R Annual = (1 + R1 )(1 + R 2 )(1 + R 3 )(1 + R 4 )(1 + R 5 ) 1 + R Annual = (1.192)(0.864)(1.010)(0.812)(1.053) = 0.89 R Annual = 0.89 - 1 = -0.11 or -11% DivYield = Divt + 1 Pt 0.03 = = 0.001, or 0.1% 21.49 Copyright © 2020 Pearson Canada Inc. 3 - 15 Example 10.2: Compounding Realized Returns: Evaluate • By repeating these steps, we have successfully computed the realized annual returns for an investor holding ABX stock over this one-year period. From this exercise, we can see that returns are risky: ABX lost 11% of its value in a single year. Copyright © 2020 Pearson Canada Inc. 3 - 16 10.2 Historical Risks and Returns of Stocks • Average Annual Returns – Average Annual Return of a Security π α = 1 (π 1 + π 2 +. . . +π π ) π Copyright © 2020 Pearson Canada Inc. (Eq. 10.3) 3 - 17 10.2 Historical Risks and Returns of Stocks • The Variance and Volatility of Returns: – Variance: A method to measure the variability of returns—the expected squared deviation of returns from the mean. πππ π = 1 α 2 + (π 2 − π ) α 2 +. . . +(π π − π ) α 2 (π 1 − π ) π−1 (Eq. 10.4) – Standard Deviation: A common method used to measure the risk of a probability distribution—the square root of the variance. ππ·(π ) = πππ π (Eq. 10.5) Copyright © 2020 Pearson Canada Inc. 3 - 18 Example 10.3: Computing Historical Volatility • Using the data from Table 10.1, what is the standard deviation of the S&P/ TSX Composite Index returns for the years 2008 to 2017? Copyright © 2020 Pearson Canada Inc. 3 - 19 Example 10.3: Computing Historical Volatility: Plan • With the 10 returns, compute the average return using Equation 10.3, because it is an input to the variance equation. Next, compute the variance using Equation 10.4 and then take its square root to determine the standard deviation. 2008 2009 2010 2011 2012 −33.00 % 35.05% 17.61% −8.71% 7.19% 2013 2014 2015 2016 2017 12.99% 10.55% −8.32% 21.08% 9.10% Copyright © 2020 Pearson Canada Inc. 3 - 20 Example 10.3: Computing Historical Volatility: Execute (1 of 2) • The average annual return of the S&P/ TSX Composite Index during this period as 6.35%, so we have al the necessary inputs for the variance calculation: Applying Eq. 10.4, we have: 1 ππ΄π (π ) = π 1 − π α 2 + π 2 − π α 2 + β― + π π − π α 2 π−1 1 = ΰ΅« −0.33 − 0.0635 2 + 0.3505 − 0.0635 10 − 1 = 0.0359 Copyright © 2020 Pearson Canada Inc. 2 + β― + (0.091 3 - 21 Example 10.3: Computing Historical Volatility: Execute (2 of 2) • Alternatively, we can break the calculation of this equation out as follows: 2008 2009 2010 2011 2012 Return −0.3300 0.3505 0.1761 −0.0871 0.0719 Average 0.0635 0.0635 0.0635 0.0635 0.0635 Difference −0.3935 0.2870 0.1126 −0.1506 0.0084 Squared 0.1548 0.0824 0.0127 0.0227 0.0001 2013 2014 2015 2016 2017 Return 0.1299 0.1055 −0.0832 0.2108 0.0910 Average 0.0635 0.0635 0.0635 0.0635 0.0635 Difference 0.0664 0.0420 −0.1467 0.1473 0.0275 Squared 0.0044 0.0018 0.0215 0.0217 0.0008 Copyright © 2020 Pearson Canada Inc. 3 - 22 Example 10.3: Computing Historical Volatility: Execute (3 of 3) • Summing the squared differences in the last row, we get 0.3228. Finally, dividing by (10 − 1 = 9) gives us 0.3228/9 = 0.0359. The standard deviation is therefore, SD( R) = Var ( R ) = 0.0359 = 0.1894, or 18.94% Copyright © 2020 Pearson Canada Inc. 3 - 23 Example 10.3: Computing Historical Volatility: Evaluate • Our best estimate of the expected return for the S&P/TSX Composite Index is its average return, 6.35%, but it is risky, with a standard deviation of 18.94%. Copyright © 2020 Pearson Canada Inc. 3 - 24 Suggested Homework • • • • Use Coca-Cola’s dividend history from here: https://www.streetinsider.com/dividend_history.php?q=ko And its share price history from here: https://finance.yahoo.com/quote/KO/history?ltr=1 To calculate annualized return from holding a Coca-Cola stock from 2011 to 2021 (Jan 1, 2012 – Dec 31, 2021) Use the annualized returns you calculated in the previous part to calculate the average annual return and standard deviation of annual returns for the period 2011 – 2021. Copyright © 2020 Pearson Canada Inc. 3 - 25