1 / 81

810 likes | 981 Vues

BCOR 2200 Chapter 10. Lessons From Capital Market History. We already know : Capital budgeting requires calculating the NPV: Discounting future Cash Flows (Numerator) At the Require Rate of Return (Denominator) We also know : Which Cash Flows to use… Use the Stand-Alone Principle

Télécharger la présentation
## BCOR 2200 Chapter 10

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**BCOR 2200Chapter 10**Lessons From Capital Market History**We already know :**Capital budgeting requires calculating the NPV: • Discounting future Cash Flows (Numerator) • At the Require Rate of Return (Denominator) We also know : • Which Cash Flows to use… • Use the Stand-Alone Principle • Use Incremental Cash Flows associated with: • Operations (OCF) • Capital Spending (NCS) • Working Capital (DNWC) • Test the CF forecasts used to calculate the NPV • Sensitivity and Scenario analysis Now we will start looking at the Required Rate of Return **The General Idea:**• The appropriate discount rate for a project (or a company) • Reflects the project’s risk • The riskier the project, the higher the required return • Why? Investors are RISK AVERSE • So how do we measure the project’s risk? • And once we know the risk, what is the correct rate of return for that risk?**Start with this Assumption:**• The new project has the SAME risk as the firm’s current projects • Then we can use the rate or return firm is currently paying • But how do we calculate that? • Later: What if the new project’s risk isdifferent, • We can adjust the use the rate or return firm is currently paying to account for difference in risk • So we will look at: • The general historic risk and return for all companies (the market) • The risk and return for different types of companies • The risk for the company we’re analyzing**Chapter Outline:**• The Mechanics of Calculating Returns • Dollar Returns • Percent Returns • The Historical Record • Calculating Average Returns • Return Variability (Risk) • More about Calculating Average Returns • Market Efficiency**10.1 Returns**Dollar Returns: Bond Example: • You bought a bond for $950 1 year ago. • You have received two coupons of $30 each. • You can sell the bond for $975 today. • Calculate your total dollar return: • Income = $30 + $30 = $60 • Capital gain = $975 – $950 = $25 • Total dollar return = $60 + $25 = $85**Dollar Returns:**Stock Example: • 1 year ago, you bought stock for $50 per share. • You received 4 dividends of $1.25 each • Today the price of the stock is $48 • Calculate your total dollar return: • Income = 4($1.25) =$5.00 • Capital gain = $48 – $50 = -$2.00 • Total dollar return = $5.00 – $2.00 = $3.00**Percent Returns:**Of course dollar returns aren’t very useful! New Stock Example: • 1 year ago, you bought stock for $100 per share. • You received 4 dividends of $1.25 each • Today the price of the stock is $98 • Calculate your total dollar return: • Income = 4($1.25) =$5.00 • Capital gain = $98 – $100 = -$2.00 • Total dollar return = $5.00 – $2.00 = $3.00 • Dollar returns are the same for $50 and $100 stocks! • Make $3.00 on $100 vs. Make $3 on $50 • We can see this is 3% vs. 6%**Percent Return Formula**A little Algebra:**Percent Return Formula**Total Return = (P1 + D1)/ P0 - 1 • A stock costs $100 today. • One year ago is was $90. • It paid a $3 dividend today • Calculate the return over the last year: Total Return = R = ($100 + $3)/$90 - 1 = 1.1444 – 1 = 0.1444 = 14.44% Note: $90(1 + R) = $90(1.1444) = $103**Clicker Question:**• A stock’s current market price is $50. It just paid a $2.00 dividend. One year ago, the stock cost $40 • Calculate: • the stock’s Dividend Yield • the stock’s Capital Gain Yield • the stock’s Total Return**Clicker Answer:**• P1 = $50 D1 = $2.00 P0 = $40 • Div Yld = D1/P0 = $2.00/$40 = 5% • Cap Gain Yld = P1/P0 – 1 = $50/$40 – 1 = 25% • Total Return = (P1 + D1)/P0 – 1 = ($50 + $2)/$40 – 1 = 30% -OR- • Total Return = Div Yld + Cap Gain Yld = 5% + 25% = 30% The Answer is D**Clicker Question:**• A stock’s current price is $80. It is expected to pay a $4.00 dividend in one year. The expected price in one year is $70 • Calculate: • the stock’s expectedDividend Yield • the stock’s expectedCapital Gain Yield • the stock’s expected Total Return**Clicker Answer:**• P1 = $70 D1 = $4.00 P0 = $80 • Div Yld = D1/P0 = $4.00/$80 = 5% • Cap Gain Yld = P1/P0 – 1 = $70/$80 – 1 = -12.5% • Total Return = (P1 + D1)/P0 – 1 = ($70 + $4)/$80 – 1 = -7.5% -OR- • Total Return = Div Yld + Cap Gain Yld = 5% + -12.5% = -7.5% The Answer is B**10.2 The Historical Record**• Why do we look at the historical record? • Do we care (directly) about what happened in the past? • Not really • What we do care about is the future. • So what will happen in the future? • Maybe our best guess is what has happened in the past. • So we do care - indirectly - about the past**So lets look at the Historical record:**What has happened to: • Large Stocks • Small Stocks • Corporate Bonds • Long-Term Government debt (T-Bonds) • Short-Term Government debt (T-Bills) • Securities trade in financial markets • And market prices allow us to measure past returns and risk for different securities • So we’ll look at: • the historic returns • the variation in historic returns • Variance and Standard Deviation**Financial Markets:**• Match SAVERS of funds with USERS of funds • Savers of funds invest in financial assets • They can defer consumption (Save!) • And earn a return to compensate for the deferred consumption • Users have access to unused capital • Theycan invest in productive assets (Invest!) • IF… They can earn enough from those assets to pay the return required by savers • We’ll examine financial markets to provide us with information about the returns savers require for various levels of risk • Based on the type of security**We’ll look at 5 types of Securities:**• Large-Company Stocks • The S&P 500 • Small-Company Stocks • Bottom 20% of NYSE by market cap • So really “smaller” stocks • These are still NYSE stocks, so not that small • Reread pages 217 to 219 and the box on page 221 • Long-Term, High-Quality Corporate Bonds • 20 years to maturity • Long-Term US Government Bonds • 20 year T-bonds • US Treasury Bills • 3 month T-bills**Large Stocks Returns**• Figures 10.5 and 10.6 • Note the Different Scales • Note the correlation between returns Small Stocks Returns**Figure 10.7**• Again note the Different Scales • T-Bonds -10% to 50%, T-bills 0 to 16% (never negative) • Again note the correlation between returns T-Bond Returns T-Bill Returns**Figure 10.8**• Annual Inflation • Again note Scale Inflation**Further discussion on the historical record:**• Read Page 315 through 321 • See Figures 10.5 through 10.8 and Tables 10.1 through 10.3 • Asset Classes: • Large stocks • Small Stocks • Long-term Corporate Bonds • Long-term Government Bonds • U.S. Treasury Bills • Inflation • Get an idea of large and small changes for each of these categories • How is inflation measured?**10.3 Average Returns of Investment Categories**RReal = (1 + RNom)/(1 + i) – 1 = (1 +0.1180)/(1.0310) - 1 = 8.44% Risk Premium = RNom– Risk-Free = 0.1180 – 0.0360 = 8.20% (T-Bills are risk-free) Data is shown in Tables 10.2 and 10.3**Average Returns**RReal = (1 + RNom)/(1 + Inflation) – 1 For Small Stocks: RNom = 16.5% RReal = 13.0% MoneyDoubled in Small Stocks: • Rule of 72’s: 72/16.5 = 4.36 years • PV = -1; FV = 2; I/Y = 16.5; N = 4.54 • =nper(rate, pmt, pv, [fv],[type]) • =nper(.165,0,-1,2) = 4.54**Average Returns**RReal = (1 + RNom)/(1 + Inflation) – 1 For Small Stocks: RNom = 16.5% RReal = 13.0% Purchasing Power Doubled in Small Stocks: • Rule of 72’s: 72/13.0 = 5.54 years • PV = -1; FV = 2; I/Y = 13.0; N = 5.67 • =nper(rate, pmt, pv, [fv],[type]) • =nper(.130,0,-1,2) = 5.67**Risk Premium**• The amount of return earned over the risk-free rate: • T-bills are risk free (Why?) Risk Premium = Average Return - Average T-bill Return • This is the compensation for incurring risk associated with this investment class • Make sure you can distinguish Risk Premium from Real Return Average Risk Premium: Large stocks 11.8% – 3.6% = 8.2% Small stocks 16.5% – 3.6% = 12.9% L-T corporate bonds 6.4% – 3.6% = 2.8% L-T government bonds 6.1% – 3.6% = 2.5% Risk Premium is a RETURN measure, not a risk measure**10.4 Variability of Returns (Risk)**Recall Figure 10.4: • Why would you own anything but small stocks? • Since the return is higher • Because the variability is also higher • If you have a short investment horizon… • You could lose large amount in that short period • How much could you lose in T-Bills over a short period? • Nothing (or not very much?) • This is the essence of the risk-return trade-off**Risk: A Picture of the Dispersion of Returns**Start with a Frequency Distribution for Large Stocks (Fig 10.9): Calculate Returns since 2009:**Risk: A Picture of the Dispersion of Returns**Start with a Frequency Distribution for Large Stocks (Fig 10.9): Calculate Returns since 2009: 2009**Risk: A Picture of the Dispersion of Returns**Start with a Frequency Distribution for Large Stocks (Fig 10.9): Calculate Returns since 2009: 2010 2009**Risk: A Picture of the Dispersion of Returns**Start with a Frequency Distribution for Large Stocks (Fig 10.9): Calculate Returns since 2009: 2010 2009 2011**Risk: A Picture of the Dispersion of Returns**Start with a Frequency Distribution for Large Stocks (Fig 10.9): Calculate Returns since 2009: 2012 2010 2009 2011**Risk: A Picture of the Dispersion of Returns**Start with a Frequency Distribution for Large Stocks (Fig 10.9): Calculate Returns since 2009: 2012 2010 2013 2009 2011**Risk: Dispersion of Returns**Calculating a Number • Measures of Dispersion: Variance and Standard Deviation Recall: • Variance is the sum of the squared deviations from the mean • Standard Deviation is the square-root of the Variance Why divided the sum by T – 1 and not T when calculating Variance?**How to Calculate Variance (s2) and Stdev (s)**Mean Return = 0.42/4 = 0.105 = 10.5% s2 = (Sum of Squared Deviations)/(T – 1) = 0.0045/(4 – 1) = 0.0015 s = Square Root of Variance = (0.0015)½ = 0.0387 = 3.87% • The Standard Deviation is in the SAME units as the variable • In this case % return, so it can be expresses as a % • Variance is NOT, so it can not be expressed as a %**Example 10.2 page 315**How to Calculate Variance (s2) and Stdev (s): Mean Return = 0.16/4 = 0.04 = 4% s2 = (Sum of Squared Deviations)/(T – 1) = 0.0270(4 – 1) = 0.009 s = Square Root of Variance = (0.009)½ = 0.0949 = 9.49%**Mean and Standard Deviation of Historic Returns**Date is shown in Figure 10.10 on page 327**Interpreting the Distribution Measure (s)**• What does s mean? • It depends… • If we assume that the data is from a Normal Distribution • Then s tells us a lot • See the Normal Distribution and Statistics Review on the website • Recall for the Normal Distribution: • Mean +/- 1s contains approximately 68% of the observations • Really 68.26% • Mean +/- 2s contains approximately 95% of the observations • Really 95.44% • Mean +/- 3s contains approximately 99% of the observations • Really 99.73%**Interpreting the Distribution Measure (s)**For the Large Stock Portfolio: • Mean Return = 11.8% • Standard Deviation (s) = 20.3% • 68% of observations between 11.8% +/- 1 x20.3% • Between -8.5% and 32.1% • 95% of observations between 11.8% +/- 2x 20.3% • Between -28.8% to 52.4% • 99% of observations between 11.8% +/- 3x 20.3% • Between -49.1% to 72.7% Notice you can be MORE CONFIDENT about a WIDER interval!**Normal Distribution**• A large enough sample drawn from a normal distribution looks like a bell-shaped curve. Probability The probability that an annual return will fall within -8.5% and 32.1% is 68.26% (approximately 2/3). + 3s72.7% - 3s- 49.1% - 2s- 28.8% - 1s - 8.5% 011.5% + 1s32.1% + 2s52.4% Return onlarge company commonstocks 68% 95% 99%**Return Distributions (Risk) for Different Invest Classes:**95%**Clicker Question:**• The expected return of a stock is 15% and it’s standard deviation is 18% • What will be the range of returns with 68% confidence? • What will be the range of returns with 95% confidence?**Clicker Answer:**• 68% confidence is within the mean plus or minus one standard deviation: 15% - 18% = -3% 15% + 18% = 33% • 95% confidence is within the mean plus or minus two standard deviation: 15% - 2(18%) = -21% 15% + 2(18%) = 51% The Answer is A**Return Probabilities Assuming Normality**Another thing we can do: • Large Stock Mean = 11.8% and σ = 20.3% • Calculate the probability of a negative return in large stocks • P(R < 0) = ? How far from the mean is 0? • How many stdevs to the left of the mean to get to 0? • z = (x – mean)/σ = (0 – 0.118)/0.203 = -0.581 • So a little more than ½ a stdev from the mean to 0 How much of the curve is to the left of the mean - 0.568σ? • =NORMDIST(x, mean, standard_dev, cumulative) • =NORMDIST(0,0.118,0.203,1) = 0.2805 = 28.05% 28.05% chance of a negative return next year in large stocks**Return Probabilities Assuming Normality**Another way to do it: • Large Stock Mean = 11.8% and σ = 20.3% • Calculate the probability of a negative return in large stocks How far from the mean is 0? • How many stdevs to the left of the mean to get to 0? • z = (x – mean)/σ = (0 – 0.118)/0.203 = -0.581 How much of the curve is to the left of the mean - 0.581σ? • =NORM.S.DIST(z,1) • =NORM.S.DIST(-.581,1) = 0.2806 = 28.05% NORM.DIST: Enter x, mean and σ NORM.S.DIST: Enter only z**Return Probabilities Assuming Normality**One more example: • Large Stock Mean = 11.8% and σ = 20.3% • Calculate the probability earning at least 50% (R > 50%) How far from the mean is 50%? • How many stdevs to the right of the mean to get to 50%? • z = (x – mean)/σ = (0.50 – 0.118)/0.203 = 0.382/0.203 = 1.88 How much of the curve is to the RIGHT of the mean + 1.88σ? • =NORM.S.DIST(z,1) • =NORM.S.DIST(1.88,1) = 0.9701 = 97.01% • 97.01% to the left or right? • So what is the probability of earnings more then 50%? • P(R > 50%) = 1 – 0.9701 = 2.99%**Return Probabilities Assuming Normality**Last example: • Large Stock Mean = 11.8% and σ = 20.3% • Calculate the probability earning between10% and 30% How far from the mean is 10%? • z = (x – mean)/σ = (0.10 – 0.118)/0.203 = -0.018/0.203 = -.0887 • =NORM.S.DIST(-0.0887) = 0.4647 • P(R < 10%) = 46.47% How far from the mean is 30%? • z = (x – mean)/σ = (0.30– 0.118)/0.203 = 0.182/0.203 = 0.8966 • =NORM.S.DIST(0.8966) = 0.8150 • P(R < 30%) = 81.50% P(R < 10%) = 46.47% P(R < 30%) = 81.50% P(R > 10%andR < 30%) =81.50%-44.47%= 35.03%

More Related