Risk and Return: Past and Prologue
Download
1 / 34

Risk and Return: Past and Prologue - PowerPoint PPT Presentation


  • 168 Views
  • Uploaded on

Risk and Return: Past and Prologue. 5. Bodie, Kane, and Marcus Essentials of Investments, 9th Edition. 5.1 Rates of Return. Holding-Period Return (HPR) Rate of return over given investment period HPR= [PS − PB + CF] / PB PS = Sale price PB = Buy price

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Risk and Return: Past and Prologue' - booth


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Risk and Return: Past and Prologue

5

Bodie, Kane, and Marcus

Essentials of Investments, 9th Edition


5 1 rates of return
5.1 Rates of Return

  • Holding-Period Return (HPR)

    • Rate of return over given investment period

  • HPR= [PS − PB + CF] / PB

    • PS = Sale price

    • PB = Buy price

    • CF = Cash flow during holding period


5 1 rates of return1
5.1 Rates of Return

  • Measuring Investment Returns over Multiple Periods

    • Arithmetic average

      • Sum of returns in each period divided by number of periods

    • Geometric average

      • Single per-period return; gives same cumulative performance as sequence of actual returns

      • Compound period-by-period returns; find per-period rate that compounds to same final value

    • Dollar-weighted average return

      • Internal rate of return on investment



5 1 rates of return2
5.1 Rates of Return Fund

  • Conventions for Annualizing Rates of Return

    • APR = Per-period rate × Periods per year

      • 1 + EAR = (1 + Rate per period)

      • 1 + EAR = (1 + Rate per period)n= (1 + )n

      • APR = [(1 + EAR)1/n– 1]n

      • Continuous compounding: 1 + EAR = eAPR

APR

n


5 2 risk and risk premiums
5.2 Risk and Risk Premiums Fund

  • Scenario Analysis and Probability Distributions

    • Scenario analysis: Possible economic scenarios; specify likelihood and HPR

    • Probability distribution: Possible outcomes with probabilities

    • Expected return: Mean value of distribution of HPR

    • Variance: Expected value of squared deviation from mean

    • Standard deviation: Square root of variance





5 2 risk and risk premiums2
5.2 Risk and Risk Premiums Standard Deviation 20%

  • Normality over Time

    • When returns over very short time periods are normally distributed, HPRs up to 1 month can be treated as normal

    • Use continuously compounded rates where normality plays crucial role


5 2 risk and risk premiums3
5.2 Risk and Risk Premiums Standard Deviation 20%

  • Deviation from Normality and Value at Risk

    • Kurtosis: Measure of fatness of tails of probability distribution; indicates likelihood of extreme outcomes

    • Skew: Measure of asymmetry of probability distribution

  • Using Time Series of Return

    • Scenario analysis derived from sample history of returns

    • Variance and standard deviation estimates from time series of returns:


Figure 5.2 Comparing Scenario Analysis to Normal Distributions with Same Mean and Standard Deviation


5 2 risk and risk premiums4
5.2 Risk and Risk Premiums Distributions with Same Mean and Standard Deviation

  • Risk Premiums and Risk Aversion

    • Risk-free rate: Rate of return that can be earned with certainty

    • Risk premium: Expected return in excess of that on risk-free securities

    • Excess return: Rate of return in excess of risk-free rate

    • Risk aversion: Reluctance to accept risk

    • Price of risk: Ratio of risk premium to variance


5 2 risk and risk premiums5
5.2 Risk and Risk Premiums Distributions with Same Mean and Standard Deviation

  • The Sharpe (Reward-to-Volatility) Ratio

    • Ratio of portfolio risk premium to standard deviation

  • Mean-Variance Analysis

    • Ranking portfolios by Sharpe ratios


5 3 the historical record
5.3 The Historical Record Distributions with Same Mean and Standard Deviation

  • World and U.S. Risky Stock and Bond Portfolios

    • World Large stocks: 24 developed countries, about 6000 stocks

    • U.S. large stocks: Standard & Poor's 500 largest cap

    • U.S. small stocks: Smallest 20% on NYSE, NASDAQ, and Amex

    • World bonds: Same countries as World Large stocks

    • U.S. Treasury bonds: Barclay's Long-Term Treasury Bond Index


Figure 5 4 rates of return on stocks bonds and bills
Figure 5.4 Rates of Return on Stocks, Bonds, Distributions with Same Mean and Standard Deviationand Bills


5 4 inflation and real rates of return
5.4 Inflation and Real Rates of Return Distributions with Same Mean and Standard Deviation

  • Equilibrium Nominal Rate of Interest

    • Fisher Equation

      • R = r + E(i)

      • E(i): Current expected inflation

      • R: Nominal interest rate

      • r: Real interest rate


5 4 inflation and real rates of return1
5.4 Inflation and Real Rates of Return Distributions with Same Mean and Standard Deviation

  • U.S. History of Interest Rates, Inflation, and Real Interest Rates

    • Since the 1950s, nominal rates have increased roughly in tandem with inflation

    • 1930s/1940s: Volatile inflation affects real rates of return



5 5 asset allocation across portfolios
5.5 Asset Allocation across Portfolios Rates 1926-2010

  • Asset Allocation

    • Portfolio choice among broad investment classes

  • Complete Portfolio

    • Entire portfolio, including risky and risk-free assets

  • Capital Allocation

    • Choice between risky and risk-free assets


5 5 asset allocation across portfolios1
5.5 Asset Allocation across Portfolios Rates 1926-2010

  • The Risk-Free Asset

    • Treasury bonds (still affected by inflation)

    • Price-indexed government bonds

    • Money market instruments effectively risk-free

    • Risk of CDs and commercial paper is miniscule compared to most assets


5 5 asset allocation across portfolios2
5.5 Asset Allocation Across Portfolios Rates 1926-2010

  • Portfolio Expected Return and Risk

    P: portfolio composition

    y: proportion of investment budget

    rf: rate of return on risk-free asset

    rp: actual rate of return

    E(rp): expected rate of return

    σp: standard deviation

    E(rC): return on complete portfolio

    E(rC) = yE(rp) + (1 − y)rf

    σC = yσrp+ (1 − y)σrf



5 5 asset allocation across portfolios3
5.5 Asset Allocation across Portfolios Rates 1926-2010

  • Capital Allocation Line (CAL)

    • Plot of risk-return combinations available by varying allocation between risky and risk-free

  • Risk Aversion and Capital Allocation

    • y: Preferred capital allocation


5 6 passive strategies and the capital market line
5.6 Passive Strategies and the Capital Market Line Rates 1926-2010

  • Passive Strategy

    • Investment policy that avoids security analysis

  • Capital Market Line (CML)

    • Capital allocation line using market-index portfolio as risky asset



5.6 Passive Strategies and the Capital Market Line Rates 1926-2010

  • Cost and Benefits of Passive Investing

    • Passive investing is inexpensive and simple

    • Expense ratio of active mutual fund averages 1%

    • Expense ratio of hedge fund averages 1%-2%, plus 10% of returns above risk-free rate

    • Active management offers potential for higher returns


Selected Problems Rates 1926-2010

5-28


Problem 1
Problem 1 Rates 1926-2010

$140,710.04

  • V(12/31/2004) = V (1/1/1998) x (1 + GAR)7

    = $100,000 x (1.05)7 =

5-29


Problem 2
Problem 2 Rates 1926-2010

(50 – 40 + 2)/40 = 0.30 = 30.00%

(43 – 40 + 1)/40 = 0.10 = 10.00%

(34 – 40 + 0.50)/40 = –0.1375 = –13.75%

[(1/3) x 30%] + [(1/3) x 10%] + [(1/3) x (–13.75%)] = 8.75%

0.031979

a. The holding period returns for the three scenarios are:

Boom:

Normal:

Recession:

E(HPR) =

2(HPR)

5-30


Problem 2 cont
Problem 2 Cont. Rates 1926-2010

Risky E[rp] = 8.75%Risky p = 17.88%

(0.5 x 8.75%) + (0.5 x 4%) = 6.375%

0.5 x 17.88% = 8.94%

b. E(r) =

 =

5-31


Problems 3 4
Problems 3 & 4 Rates 1926-2010

3. For each portfolio: Utility = E(r) – (0.5  4 2 )

We choose the portfolio with the highest utility value, which is Investment 3.

5-32


Problems 3 4 cont
Problems 3 & 4 Cont. Rates 1926-2010

0

highest expected return

Investment 4

4. When an investor is risk neutral, A = _ so that the portfolio with the highest utility is the portfolio with the _______________________.

So choose ____________.

5-33


Problem 5
Problem 5 Rates 1926-2010

Time

Cash flow

Explanation

0

1

2

3

b. DWR

a. TWR

Year

Return = [(capital gains + dividend) / price]

a. TWR

2002-2003

(110 – 100 + 4)/100 = 14.00%

-300

Purchase of three shares at $100 per share

2003-2004

(90 – 110 + 4)/110 = –14.55%

-208

Purchase of two shares at $110,

plus dividend income on three shares held

2004-2005

(95 – 90 + 4)/90 = 10.00%

3.15%

110

Dividends on five shares,

plus sale of one share at $90

396

Dividends on four shares,

plus sale of four shares at $95 per share

2.33%

-0.1661%

5-34


ad