# Chapter 2 Measuring Return and Risk - PowerPoint PPT Presentation

PPT – Chapter 2 Measuring Return and Risk PowerPoint presentation | free to download - id: 29f97e-ZDc1Z

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Chapter 2 Measuring Return and Risk

Description:

### Returns based on a time series of historical data. Investment decisions largely based on ... defined as unanticipated changes in prices and cash flows over time. ... – PowerPoint PPT presentation

Number of Views:44
Avg rating:3.0/5.0
Slides: 29
Provided by: davidpec
Category:
Tags:
Transcript and Presenter's Notes

Title: Chapter 2 Measuring Return and Risk

1
Chapter 2Measuring Return and Risk
• Measuring Returns
• Measuring Risk
• Distributions

2
Learning Objectives
• Sources of Investment Returns
• Measures of Investment Returns
• Sources of Investment Risk
• Measures of Investment Risk
• Monte Carlo Simulation
• Investment Performance and Margin

3
Sources of Investment returns
• Dividends, Interest
• Cash dividends on common, preferred stock
• Interest (coupons) on Bills and Bonds
• Capital gains/losses (Realized vs. Paper)
• Increases/decreases in price
• Other
• Stock Dividends
• Rights and Warrants

4
Returns on Investment
• Ex Ante Returns
• Returns derived from a probability distribution
• Based on expectations about future cash flows
• Ex Post Returns
• Returns based on a time series of historical data
• Investment decisions largely based on ex post
analysis modified by ex ante expectations

5
Measuring Returns
• Holding Period Returns (HPR) Eq. 2-1

Where Pt current price Pt-1 purchase
price CFt cash flow received in time t HPR
normally computed on monthly basis
6
Measuring Returns
• Holding Period Return Relative (HPRR) Eq. 2-2
• HPR HPRR - 1

7
Measuring Returns
• Per-Period Return (PPR) Eq. 2-3
• Return earned for particular period (for example,
annual return)
• Per-Period Return (Periods Income Price
Change) ? Beginning Period Value
• Per-Period Return Relative (PPRR) Eq. 2-3a
• Per-Period Return Relative (Periods Income
End of Period Value) ? Beginning Period Value
• PPR PPRR - 1

8
Compounding
• Computing Future Values given a ROR
• FV Begin Value (1 ROR)t Eq. 2-4
• Where t number of periods
• ROR assumed Rate of Return
• (1 ROR)t Future Value Interest Factor (FVIF)
• FV is also termed Ending Value
• Example What is the future value of 10,000
invested for 10 years if the ROR is 8?
• FV 10,000 (1.08)10 21,589.25

9
Compounding
• Computing the Effective Annual Rate
• Rear (1 HPR)12/n -1
• Example You realize a 6.5 return over a 4 month
period. What is the EAR
• (1.065)12/4 - 1 0.2079 20.79 per annum

10
Measuring Average Returns
• Average Rate of Return (AROR) as Arithmetic
Average

11
Measuring Geometric Returns
• Geometric Returns as Product (P)

GHPR as a mean geometric holding period
return Arithmetic Average Returns upwardly biased
12
Expected Returns
• Probability Distributions
• Normal
• Leptokurtic
• Platykurtic
• Skewed
• Expected Returns are State of Nature specific
probability assignments

13
Portfolio Expected Returns
• Weighted Average Rate of Return
• WARR W1 x E(R1) W2 x E(R2) . . . Wn x
E(Rn)
• where Wi of portfolio invested in security i
• E(Ri) expected per-period return for security i
• Subject to W1 Wn 1

14
Risk and return
• What is risk?
• Uncertainty - the possibility that the actual
return may differ from the expected return
• Probability - the chance of something occurring
• Expected Returns - the sum of possible returns
times the probability of each return

15
Types of Risk
• Pure Risk
• Involves only chance of loss or no loss
• Casualty insurance is a good example
• Moral Hazard Problem
• Speculative Risk
• Associated with speculation in which there is
some chance of gain and some chance of loss

16
Sources of Risk
• Investment Theory Market Risk
• Diversifiable vs. Non-Diversifiable (CAPM)
• Purchasing Power impact of inflation
• Real vs. Nominal Returns
• Interest Rate Risk
• Changes in market values when rates change
• Price risk vs. Reinvestment Rate Risk

17
Sources of Investment Risk
• Financial Risk
• Default, Liquidity, Marketability, Leverage
• Exchange Rate Risk Political Risk
• Tax Risk (changes in code, treatment)
• Investment Manager Risk

18
Measures of Risk
• Standard Deviation
• Coefficient of Variation CV SD / Mean
• Beta (CAPM relative risk market)
• Range highest to lowest expected values
• Semi-Variance (trimmed mean)

19
Measuring Risk
• Finance
• Standard Deviation (SD)

20
Risk and Return
• Fundamental Relationship
• The greater the risk, the greater the expected
return (positively related)
• Investors assumed to be risk averse
• The will want the same return with less risk.
• Assume greater risk only for greater returns.
• Risk and Return relationship varies over time.

21
Monte Carlo Simulation
• Dealing with random nature of returns
• Use of random numbers (probabilities) to vary
expected future outcomes.
• Computer programs will generate numbers between 0
and 1. Output range can be set
• Example only values between 0 and .25
• Random effects may be positive or negative
(requires two draws)

22
• Margin rate percentage of securities purchase
that must come from investors funds rather than
from borrowing
• Initial margin rate used when determining cash
needed for new purchase
• Maintenance margin rate used when determining if
margin call is needed

23
• Margin Rates
• Federal Reserve Board vs. In-house rule
• Regulation T
• 50 initial margin rate
• NYSE's Rule 431 FINRA's Rule 2520
• 25 maintenance margin rate MMR
• 30 on short positions
• In-house requirements may be higher, never lower

24
• Dollar value of additional securities that can be
purchased on margin with current equity in margin
account
• BP a function of Net Equity position
• E MV Loan
• BP (E / IMR) MV
• See examples 1 and 2 on page 2.44-.45

25
• Margin Calls
• M/C Threshold Loan Value / (1 MMR)
• Example MMR 25, Loan 50,000
• M/C T 50,000 / (.75) 66,667.
• If value of portfolio drops below 66,667
broker calls for Cash Required Loan
MV(1-MMR)
• Meeting Margin calls
• Deposit (or transfer additional funds)
• Liquidate a portion of portfolio proceeds to
pay down

26
• Effects of Margin Buying on Investment Returns
• ROI (50000 40000) / 40000 25
• 50 Margin (50000 40000) / 20000 50
• ROI (50000 60000) / 60000 - 16.66
• ROI (50000 60000) / 30000 - 33.33

27