Fm10e ch06
Upcoming SlideShare
Loading in...5
×
 

 

Statistics

Views

Total Views
323
Views on SlideShare
323
Embed Views
0

Actions

Likes
0
Downloads
5
Comments
0

0 Embeds 0

No embeds

Accessibility

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Fm10e ch06 Fm10e ch06 Presentation Transcript

    • Chapter 6 - Risk and Rates of Return  2005, Pearson Prentice Hall
    • Chapter 6: Objectives
      • Inflation and rates of return
      • How to measure risk
      • (variance, standard deviation, beta)
      • How to reduce risk
      • (diversification)
      • How to price risk
      • (security market line, Capital Asset Pricing Model)
    • Inflation, Rates of Return, and the Fisher Effect Interest Rates
    • Interest Rates Conceptually :
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf =
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k*
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* +
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically :
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically : (1 + k rf ) = (1 + k*) (1 + IRP)
    • Interest Rates Conceptually : Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically : (1 + k rf ) = (1 + k*) (1 + IRP) This is known as the “ Fisher Effect ”
      • Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium?
      • (1 + k rf ) = (1 + k*) (1 + IRP)
      • (1.08) = (1.03) (1 + IRP)
      • (1 + IRP) = (1.0485), so
      • IRP = 4.85%
      Interest Rates
    • Term Structure of Interest Rates
      • The pattern of rates of return for debt securities that differ only in the length of time to maturity.
    • Term Structure of Interest Rates
      • The pattern of rates of return for debt securities that differ only in the length of time to maturity.
      yield to maturity time to maturity (years)
    • Term Structure of Interest Rates
      • The pattern of rates of return for debt securities that differ only in the length of time to maturity.
      yield to maturity time to maturity (years)
    • Term Structure of Interest Rates
      • The yield curve may be downward sloping or “inverted” if rates are expected to fall.
      yield to maturity time to maturity (years)
    • Term Structure of Interest Rates
      • The yield curve may be downward sloping or “inverted” if rates are expected to fall.
      yield to maturity time to maturity (years)
    • For a Treasury security, what is the required rate of return?
    • For a Treasury security, what is the required rate of return? Required rate of return =
    • For a Treasury security, what is the required rate of return?
      • Since Treasuries are essentially free of default risk , the rate of return on a Treasury security is considered the “ risk-free ” rate of return.
      Required rate of return = Risk-free rate of return
    • For a corporate stock or bond , what is the required rate of return?
    • For a corporate stock or bond , what is the required rate of return? Required rate of return =
    • For a corporate stock or bond , what is the required rate of return? Required rate of return = Risk-free rate of return
    • For a corporate stock or bond , what is the required rate of return?
      • How large of a risk premium should we require to buy a corporate security?
      Required rate of return = + Risk-free rate of return Risk premium
    • Returns
      • Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc.
      • Required Return - the return that an investor requires on an asset given its risk and market interest rates.
    • Expected Return
      • State of Probability Return
      • Economy (P) Orl. Utility Orl. Tech
      • Recession .20 4% -10%
      • Normal .50 10% 14%
      • Boom .30 14% 30%
      • For each firm, the expected return on the stock is just a weighted average :
      • State of Probability Return
      • Economy (P) Orl. Utility Orl. Tech
      • Recession .20 4% -10%
      • Normal .50 10% 14%
      • Boom .30 14% 30%
      • For each firm, the expected return on the stock is just a weighted average :
      • k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn
      Expected Return
    • Expected Return
      • State of Probability Return
      • Economy (P) Orl. Utility Orl. Tech
      • Recession .20 4% -10%
      • Normal .50 10% 14%
      • Boom .30 14% 30%
      • k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn
      • k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10%
    • Expected Return
      • State of Probability Return
      • Economy (P) Orl. Utility Orl. Tech
      • Recession .20 4% -10%
      • Normal .50 10% 14%
      • Boom .30 14% 30%
      • k = P(k 1 )*k 1 + P(k 2 )*k 2 + ...+ P(k n )*kn
      • k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14%
      • Based only on your expected return calculations, which stock would you prefer?
    • RISK? Have you considered
    • What is Risk?
      • The possibility that an actual return will differ from our expected return.
      • Uncertainty in the distribution of possible outcomes.
    • What is Risk?
      • Uncertainty in the distribution of possible outcomes.
    • What is Risk?
      • Uncertainty in the distribution of possible outcomes.
      Company A return
    • What is Risk?
      • Uncertainty in the distribution of possible outcomes.
      return Company B Company A return
    • How do We Measure Risk?
      • To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year.
      52 weeks Yld Vol Net Hi Lo Sym Div % PE 100s Hi Lo Close Chg 134 80 IBM .52 .5 21 143402 98 95 95 49 -3 115 40 MSFT … 29 558918 55 52 51 94 -4 75
    • How do We Measure Risk?
      • A more scientific approach is to examine the stock’s standard deviation of returns.
      • Standard deviation is a measure of the dispersion of possible outcomes .
      • The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk.
    • Standard Deviation
      • = (k i - k) 2 P(k i )
       n i =1 
      • Orlando Utility, Inc.
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Utility, Inc.
      • ( 4% - 10%) 2 (.2) = 7.2
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Utility, Inc.
      • ( 4% - 10%) 2 (.2) = 7.2
      • (10% - 10%) 2 (.5) = 0
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Utility, Inc.
      • ( 4% - 10%) 2 (.2) = 7.2
      • (10% - 10%) 2 (.5) = 0
      • (14% - 10%) 2 (.3) = 4.8
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Utility, Inc.
      • ( 4% - 10%) 2 (.2) = 7.2
      • (10% - 10%) 2 (.5) = 0
      • (14% - 10%) 2 (.3) = 4.8
      • Variance = 12
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Utility, Inc.
      • ( 4% - 10%) 2 (.2) = 7.2
      • (10% - 10%) 2 (.5) = 0
      • (14% - 10%) 2 (.3) = 4.8
      • Variance = 12
      • Stand. dev. = 12 =
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Utility, Inc.
      • ( 4% - 10%) 2 (.2) = 7.2
      • (10% - 10%) 2 (.5) = 0
      • (14% - 10%) 2 (.3) = 4.8
      • Variance = 12
      • Stand. dev. = 12 = 3.46%
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      • (-10% - 14%) 2 (.2) = 115.2
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      • (-10% - 14%) 2 (.2) = 115.2
      • (14% - 14%) 2 (.5) = 0
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      • (-10% - 14%) 2 (.2) = 115.2
      • (14% - 14%) 2 (.5) = 0
      • (30% - 14%) 2 (.3) = 76.8
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      • (-10% - 14%) 2 (.2) = 115.2
      • (14% - 14%) 2 (.5) = 0
      • (30% - 14%) 2 (.3) = 76.8
      • Variance = 192
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      • (-10% - 14%) 2 (.2) = 115.2
      • (14% - 14%) 2 (.5) = 0
      • (30% - 14%) 2 (.3) = 76.8
      • Variance = 192
      • Stand. dev. = 192 =
      = (k i - k) 2 P(k i )  n i =1 
      • Orlando Technology, Inc.
      • (-10% - 14%) 2 (.2) = 115.2
      • (14% - 14%) 2 (.5) = 0
      • (30% - 14%) 2 (.3) = 76.8
      • Variance = 192
      • Stand. dev. = 192 = 13.86%
      = (k i - k) 2 P(k i )  n i =1 
      • Which stock would you prefer?
      • How would you decide?
      • Which stock would you prefer?
      • How would you decide?
      • Orlando Orlando
      • Utility Technology
      • Expected Return 10% 14%
      • Standard Deviation 3.46% 13.86%
      Summary
      • It depends on your tolerance for risk!
      • Remember, there’s a tradeoff between risk and return.
      • It depends on your tolerance for risk!
      • Remember, there’s a tradeoff between risk and return.
      Return Risk
      • It depends on your tolerance for risk!
      • Remember, there’s a tradeoff between risk and return.
      Return Risk
    • Portfolios
      • Combining several securities in a portfolio can actually reduce overall risk .
      • How does this work?
    • Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time
    • Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time k A
    • Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time k A k B
    • What has happened to the variability of returns for the portfolio? rate of return time k A k B
    • What has happened to the variability of returns for the portfolio? rate of return time k p k A k B
    • Diversification
      • Investing in more than one security to reduce risk .
      • If two stocks are perfectly positively correlated , diversification has no effect on risk.
      • If two stocks are perfectly negatively correlated , the portfolio is perfectly diversified.
      • If you owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified?
      • YES!
      • Would you have eliminated all of your risk?
      • NO! Common stock portfolios still have risk.
    • Some risk can be diversified away and some cannot.
      • Market risk ( systematic risk) is nondiversifiable. This type of risk cannot be diversified away.
      • Company-unique risk (unsystematic risk) is diversifiable . This type of risk can be reduced through diversification.
    • Market Risk
      • Unexpected changes in interest rates.
      • Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle.
    • Company-unique Risk
      • A company’s labor force goes on strike.
      • A company’s top management dies in a plane crash.
      • A huge oil tank bursts and floods a company’s production area.
      • As you add stocks to your portfolio, company-unique risk is reduced.
      • As you add stocks to your portfolio, company-unique risk is reduced.
      portfolio risk number of stocks
      • As you add stocks to your portfolio, company-unique risk is reduced.
      portfolio risk number of stocks Market risk
      • As you add stocks to your portfolio, company-unique risk is reduced.
      portfolio risk number of stocks Market risk company- unique risk
    • Do some firms have more market risk than others?
      • Yes . For example:
      • Interest rate changes affect all firms, but which would be more affected:
      • a) Retail food chain
      • b) Commercial bank
      • Yes . For example:
      • Interest rate changes affect all firms, but which would be more affected:
      • a) Retail food chain
      • b) Commercial bank
      Do some firms have more market risk than others?
      • Note
      • As we know, the market compensates investors for accepting risk - but only for market risk . Company-unique risk can and should be diversified away.
      • So - we need to be able to measure market risk.
    • This is why we have Beta.
      • Beta: a measure of market risk.
      • Specifically, beta is a measure of how an individual stock’s returns vary with market returns.
      • It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market.
      • A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market.
      • A firm with a beta > 1 is more volatile than the market.
      The market’s beta is 1
      • A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market.
      • A firm with a beta > 1 is more volatile than the market.
        • (ex: technology firms)
      The market’s beta is 1
      • A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market.
      • A firm with a beta > 1 is more volatile than the market.
        • (ex: technology firms)
      • A firm with a beta < 1 is less volatile than the market.
      The market’s beta is 1
      • A firm that has a beta = 1 has average market risk . The stock is no more or less volatile than the market.
      • A firm with a beta > 1 is more volatile than the market.
        • (ex: technology firms)
      • A firm with a beta < 1 is less volatile than the market.
        • (ex: utilities)
      The market’s beta is 1
    • Calculating Beta
    • Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns
    • Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    • Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    • Calculating Beta -5 -15 5 10 15 -15 -10 -10 -5 5 10 15 XYZ Co. returns S&P 500 returns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Beta = slope = 1.20
    • Summary:
      • We know how to measure risk, using standard deviation for overall risk and beta for market risk.
      • We know how to reduce overall risk to only market risk through diversification .
      • We need to know how to price risk so we will know how much extra return we should require for accepting extra risk.
    • What is the Required Rate of Return?
      • The return on an investment required by an investor given market interest rates and the investment’s risk .
    • Required rate of return =
    • Required rate of return = + Risk-free rate of return
    • Required rate of return = + Risk-free rate of return Risk premium
    • market risk Required rate of return = + Risk-free rate of return Risk premium
    • market risk company- unique risk Required rate of return = + Risk-free rate of return Risk premium
    • market risk company- unique risk can be diversified away Required rate of return = + Risk-free rate of return Risk premium
      • Required
      • rate of
      • return
      Beta Let’s try to graph this relationship!
      • Required
      • rate of
      • return
      . Risk-free rate of return (6%) Beta 12% 1
      • Required
      • rate of
      • return
      . Risk-free rate of return (6%) Beta 12% 1 security market line (SML)
      • This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM).
      • Required
      • rate of
      • return
      . Risk-free rate of return (6%) Beta 12% 1 SML 0
      • Required
      • rate of
      • return
      . Risk-free rate of return (6%) Beta 12% 1 SML 0 Is there a riskless (zero beta) security?
      • Required
      • rate of
      • return
      Beta . 12% 1 SML 0 Is there a riskless (zero beta) security? Treasury securities are as close to riskless as possible. Risk-free rate of return (6%)
      • Required
      • rate of
      • return
      . Beta 12% 1 SML Where does the S&P 500 fall on the SML? Risk-free rate of return (6%) 0
      • Required
      • rate of
      • return
      . Beta 12% 1 SML Where does the S&P 500 fall on the SML? The S&P 500 is a good approximation for the market Risk-free rate of return (6%) 0
      • Required
      • rate of
      • return
      . Beta 12% 1 SML Utility Stocks Risk-free rate of return (6%) 0
      • Required
      • rate of
      • return
      . Beta 12% 1 SML High-tech stocks Risk-free rate of return (6%) 0
    • The CAPM equation:
      • k j = k rf + j (k m - k rf )
      The CAPM equation: 
      • k j = k rf + j (k m - k rf )
      • where:
      • k j = the required return on security j,
      • k rf = the risk-free rate of interest,
      • j = the beta of security j, and
      • k m = the return on the market index.
      The CAPM equation:  
    • Example:
      • Suppose the Treasury bond rate is 6% , the average return on the S&P 500 index is 12% , and Walt Disney has a beta of 1.2 .
      • According to the CAPM , what should be the required rate of return on Disney stock?
    • k j = k rf + (k m - k rf )
      • k j = .06 + 1.2 (.12 - .06)
      • k j = .132 = 13.2%
      • According to the CAPM, Disney stock should be priced to give a 13.2% return.
      • Required
      • rate of
      • return
      . Beta 12% 1 SML 0 Risk-free rate of return (6%)
      • Required
      • rate of
      • return
      . Beta 12% 1 SML 0 Theoretically, every security should lie on the SML Risk-free rate of return (6%)
      • Required
      • rate of
      • return
      . Beta 12% 1 SML 0 Theoretically, every security should lie on the SML If every stock is on the SML, investors are being fully compensated for risk. Risk-free rate of return (6%)
      • Required
      • rate of
      • return
      . Beta 12% 1 SML 0 If a security is above the SML, it is underpriced. Risk-free rate of return (6%)
      • Required
      • rate of
      • return
      . Beta 12% 1 SML 0 If a security is above the SML, it is underpriced. If a security is below the SML, it is overpriced. Risk-free rate of return (6%)
    • Simple Return Calculations
    • Simple Return Calculations t t+1 $50 $60
    • Simple Return Calculations = = 20% P t+1 - P t 60 - 50 P t 50 t t+1 $50 $60
    • Simple Return Calculations P t+1 60 P t 50 - 1 = -1 = 20% = = 20% P t+1 - P t 60 - 50 P t 50 t t+1 $50 $60
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 Feb $63.80 Mar $59.00 Apr $62.00 May $64.50 Jun $69.00 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 Mar $59.00 Apr $62.00 May $64.50 Jun $69.00 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 Apr $62.00 May $64.50 Jun $69.00 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 May $64.50 Jun $69.00 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 Jun $69.00 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 0.000 Aug $75.00 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 0.000 Aug $75.00 0.087 Sep $82.50 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 0.000 Aug $75.00 0.087 Sep $82.50 0.100 Oct $73.00 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 0.000 Aug $75.00 0.087 Sep $82.50 0.100 Oct $73.00 -0.115 Nov $80.00 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 0.000 Aug $75.00 0.087 Sep $82.50 0.100 Oct $73.00 -0.115 Nov $80.00 0.096 Dec $86.00
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 Feb $63.80 0.100 Mar $59.00 -0.075 Apr $62.00 0.051 May $64.50 0.040 Jun $69.00 0.070 Jul $69.00 0.000 Aug $75.00 0.087 Sep $82.50 0.100 Oct $73.00 -0.115 Nov $80.00 0.096 Dec $86.00 0.075
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 0.049 Feb $63.80 0.100 0.049 Mar $59.00 -0.075 0.049 Apr $62.00 0.051 0.049 May $64.50 0.040 0.049 Jun $69.00 0.070 0.049 Jul $69.00 0.000 0.049 Aug $75.00 0.087 0.049 Sep $82.50 0.100 0.049 Oct $73.00 -0.115 0.049 Nov $80.00 0.096 0.049 Dec $86.00 0.075 0.049
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 0.049 0.012321 Feb $63.80 0.100 0.049 0.002601 Mar $59.00 -0.075 0.049 0.015376 Apr $62.00 0.051 0.049 0.000004 May $64.50 0.040 0.049 0.000081 Jun $69.00 0.070 0.049 0.000441 Jul $69.00 0.000 0.049 0.002401 Aug $75.00 0.087 0.049 0.001444 Sep $82.50 0.100 0.049 0.002601 Oct $73.00 -0.115 0.049 0.028960 Nov $80.00 0.096 0.049 0.002090 Dec $86.00 0.075 0.049 0.000676
    • (a) (b) monthly expected month price return return (a - b) 2 Dec $50.00 Jan $58.00 0.160 0.049 0.012321 Feb $63.80 0.100 0.049 0.002601 Mar $59.00 -0.075 0.049 0.015376 Apr $62.00 0.051 0.049 0.000004 May $64.50 0.040 0.049 0.000081 Jun $69.00 0.070 0.049 0.000441 Jul $69.00 0.000 0.049 0.002401 Aug $75.00 0.087 0.049 0.001444 Sep $82.50 0.100 0.049 0.002601 Oct $73.00 -0.115 0.049 0.028960 Nov $80.00 0.096 0.049 0.002090 Dec $86.00 0.075 0.049 0.000676 0.0781 St. Dev: sum, divide by (n-1), and take sq root:
    • Calculator solution using HP 10B:
      • Enter monthly return on 10B calculator, followed by sigma key (top right corner).
      • Shift 7 gives you the expected return.
      • Shift 8 gives you the standard deviation.