Risk & Return
Introduction
• Return is the motivating force for making an
investment
• Risk is inherent to all investment decisions
• Fo...
Return
• Enables comparison of alternative options
of investment
• Measures past performance
• Helps in estimating future
...
Income receivedIncome received on an investment plus
any change in market pricechange in market price (if being(if being
t...
Rate of Return of a Stock
• Returns from holding a stock
– Dividend(s)
– Capital Gain/ Loss
The stock price for Stock A was Rs. 1010 per
share 1 year ago. The stock is currently
trading at Rs. 9.509.50 per share, a...
Return of a Bond/ Debenture
• Returns of holding a Bond/ Debenture
– Interest (annually, semi-annually, quarterly,
etc.)
–...
14% Rs. 1,000 IDBI debenture was purchased
for Rs. 1050 and was sold when the price of
the security raised to Rs. 1080 at ...
Return: Single Asset
• Rate of return =
Current yield + Capital gain/loss yield
• Current yield or Dividend yield
Annual I...
Illustration
Assume that IPCL was trading at Rs. 142 per
share one year back. It declared a dividend of
60% and the price ...
Expected Return
• Return in a future period
• Future is uncertain
• If possibilities of returns and their chance of
occurr...
Expected Rate of Return
• It is the weighted average of all possible
returns multiplied by their respective
probabilities
...
Illustration
Probability distribution of rate of return on stocks of
Bharat Foods and Oriental shipping
State of Probabili...
What rate of return do you expect on yourWhat rate of return do you expect on your
investment (savings) this year?investme...
Sources of Risk
• Interest rate risk
– Change in level of interest rates
– Security prices move inversely to interest rate...
Sources of Risk…
• Business Risk
– Industry, Environment
• Financial Risk
– Use of debt financing
• Liquidity Risk
– Trans...
Measures of Risk
(Variability of Return)
• Range
– Maximum & Minimum value
• Variance / Standard deviation (historical)
va...
Illustration (historical)
Johnson & Nicholson has the following dividend per share
(DIV) and market price per share (MP) f...
Solution
• R04 = - 28.07%
• R05 = 56.2%
• R06 = 123.4%
• R07 = 52.2%
• R08 = 57%
• Mean Return = 52.0%
∀ σ2
= 2,330.63
∀ σ...
Stock Returns of Companies
Year Bajaj Auto Ltd. Hero Honda Motors Ltd.
Jul-08 18.86 17.95
Aug-08 13.13 5.94
Sep-08 1.88 7....
Chart Showing Monthly Returns
Spot Prices of Castor Oil (10 Kgs)
Nov 2008 Oct 2009
Average Monthly Spot Prices of Castor
Oil (10 Kgs)
Months Rs.
November-08 632.16
December-08 612.80
January-09 492.43
Febr...
Average Monthly Spot Prices of Castor Oil (10 Kgs)
Months Rs. Monthly Returns
November-08 632.16
December-08 612.80 -3.06%...
Risk & Expected Rate of Return
Expected return: is the weighted average of
all possible returns multiplied by their
respec...
Variance
• Variance of an asset’s return is the sum of
the squared deviations of each possible rate
of return from the exp...
Illustration
• Probability distribution of rate of return on stocks
of Bharat Foods and Oriental shipping
State of Probabi...
Risk of Expected Returns
State of
Economy
pi Ri pi Ri Ri – R (Ri – R)2
pi(Ri–R)2
Boom 0.30 25 7.5 4.5 20.24 6.075
Normal 0...
Risk of Expected Returns
State of
Economy
pi Ri pi Ri Ri – R (Ri – R)2
pi(Ri–R)2
Boom 0.30 40 12 27.0 729.0 218.7
Normal 0...
Why Standard Deviation (σ)?
• Standard deviation is a measure of
dispersion around the average (expected)
value
• Standard...
Certainty EquivalentCertainty Equivalent (CECE) is the amount
of cash someone would require with
certainty at a point in t...
Certainty equivalent > Expected value
Risk PreferenceRisk Preference
Certainty equivalent = Expected value
Risk Indifferen...
Portfolio
• A portfolio refers to a group of assets owned by
an investor
• Assets in which an investor has made investment...
RP = Σ ( Wj )( Rj )
RP is the expected return for the portfolio,
Wj is the weight (investment proportion) for the jth
asse...
Portfolio Risk: Standard
Deviation
• Standard deviation = √ variance
• Variance of the portfolio (2-security case)
σσ22
PP...
m
j=1
m
k=1
σσPP = Σ Σ Wj Wkσjk
Wj is the weight for the jth
asset in the portfolio,
Wkis the weight for the kth
asset in ...
σσ jk = σ jσ k rr jk
σjis the standard deviation of the jth
asset in the
portfolio,
σkis the standard deviation of the kth...
Portfolio Risk: Classification
Systematic (non-
diversifiable)
• Market Risk
• Inflation risk
• Interest rate risk
Non-Sys...
TotalTotal
RiskRisk
Unsystematic riskUnsystematic risk
Systematic riskSystematic risk
STDDEVOFPORTFOLIORETURN
NUMBER OF SE...
TotalTotal
RiskRisk
Unsystematic risk or DiversifiableUnsystematic risk or Diversifiable
Systematic risk or Non-Diversifia...
CAPM is a model that describes the
relationship between risk and expected
(required) return; in this model, a security’s
e...
CAPM: Expected Return
• The expected rate of return of a security:
Expected return = Risk-free rate + Risk premium
Risk pr...
1. Capital markets are efficient.
2. Homogeneous investor expectations
over a given period.
3. Risk-freeRisk-free asset re...
An index of systematic risksystematic risk.
It measures the sensitivity of a stock’s
returns to changes in returns on the ...
Beta Calculation
Beta =
N ΣXY – (Σ X) (ΣY)
N ΣX2
– (ΣX)2
Where
X = return of market
Y = return of stock
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Risk & return

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Risk & return

  1. 1. Risk & Return
  2. 2. Introduction • Return is the motivating force for making an investment • Risk is inherent to all investment decisions • For a financial manager, risk means: “uncertainty in future cash flows” • Risk should be measured, and • Discount rate should be adjusted to measure returns • Understanding the risk-return relationship is very important– helps in decision making
  3. 3. Return • Enables comparison of alternative options of investment • Measures past performance • Helps in estimating future • Two Types: – Historical or Realized return or Holding period return – Expected return
  4. 4. Income receivedIncome received on an investment plus any change in market pricechange in market price (if being(if being traded)traded), usually expressed as a percent of the beginning market pricebeginning market price (initial(initial value)value) of the investment. DDtt + (PPtt - P- Pt-1t-1 ) PPt-1t-1 R = Defining Return
  5. 5. Rate of Return of a Stock • Returns from holding a stock – Dividend(s) – Capital Gain/ Loss
  6. 6. The stock price for Stock A was Rs. 1010 per share 1 year ago. The stock is currently trading at Rs. 9.509.50 per share, and shareholders just received a Rs. 1 dividendRs. 1 dividend. What return was earned over the past year? 1.001.00 + (9.509.50 - 10.0010.00 ) 10.0010.00RR = = 5%5% Example
  7. 7. Return of a Bond/ Debenture • Returns of holding a Bond/ Debenture – Interest (annually, semi-annually, quarterly, etc.) – Change in the price (if being traded in a market)
  8. 8. 14% Rs. 1,000 IDBI debenture was purchased for Rs. 1050 and was sold when the price of the security raised to Rs. 1080 at the end of one year. What return was earned over the past year? 140140 + (1,0801,080 – 1,0501,050) 1,0501,050RR = = 16.2%16.2% Example
  9. 9. Return: Single Asset • Rate of return = Current yield + Capital gain/loss yield • Current yield or Dividend yield Annual Income/ Beginning price • Capital gain (loss) yield (End price – Beginning price) / Beginning price
  10. 10. Illustration Assume that IPCL was trading at Rs. 142 per share one year back. It declared a dividend of 60% and the price now is Rs. 176. Compute the returns: current yield and capital gain yield on IPCL stocks. Current yield: 4.23% Capital gain yield: 23.94%
  11. 11. Expected Return • Return in a future period • Future is uncertain • If possibilities of returns and their chance of occurrence can be defined i.e. probability of outcomes…
  12. 12. Expected Rate of Return • It is the weighted average of all possible returns multiplied by their respective probabilities R = expected return Ri = return for the i th possible outcome pi = probability associated with Ri n = no. of possible outcome R = ∑ pi Ri n i = 1
  13. 13. Illustration Probability distribution of rate of return on stocks of Bharat Foods and Oriental shipping State of Probability of Rate of Return (%) Economy Occurrence ABC XYZ Boom 0.20 25 30 Normal 0.50 15 8 Recession 0.30 10 -5 ABC Ltd R = 15.5% XYZ Ltd R = 8.5%
  14. 14. What rate of return do you expect on yourWhat rate of return do you expect on your investment (savings) this year?investment (savings) this year? What rate will you actually earn?What rate will you actually earn? Does it matter if it is a bank FD or equity share?Does it matter if it is a bank FD or equity share? The variability of returns from thoseThe variability of returns from those that are expected.that are expected. The possibility that actual outcome will differThe possibility that actual outcome will differ from expected outcomefrom expected outcome Defining Risk
  15. 15. Sources of Risk • Interest rate risk – Change in level of interest rates – Security prices move inversely to interest rates • Market risk – Fluctuations in the securities market • Inflation risk – Purchase power risk
  16. 16. Sources of Risk… • Business Risk – Industry, Environment • Financial Risk – Use of debt financing • Liquidity Risk – Transaction of a asset/ conversion
  17. 17. Measures of Risk (Variability of Return) • Range – Maximum & Minimum value • Variance / Standard deviation (historical) var = σ2 = 1/n Σ (Ri – R)2 σ = √σ2 • Variance (expected return) σ2 = Σ Pi (Ri – R)2
  18. 18. Illustration (historical) Johnson & Nicholson has the following dividend per share (DIV) and market price per share (MP) for the period 2003- 2008s Year DIV MP 2003 1.53 31.25 2004 1.53 20.75 2005 1.53 30.88 2006 2.00 67.00 2007 2.00 100.00 2008 3.00 154.00 What are the annual rate of returns for the last five years? How risky is the share?
  19. 19. Solution • R04 = - 28.07% • R05 = 56.2% • R06 = 123.4% • R07 = 52.2% • R08 = 57% • Mean Return = 52.0% ∀ σ2 = 2,330.63 ∀ σ = 48.28 • The standard deviation of J&N’s share of returns is quite high. • The share is very risky.
  20. 20. Stock Returns of Companies Year Bajaj Auto Ltd. Hero Honda Motors Ltd. Jul-08 18.86 17.95 Aug-08 13.13 5.94 Sep-08 1.88 7.24 Oct-08 -8.69 -14.5 Nov-08 -39.71 5.5 Dec-08 27.45 6.61 Jan-09 21.14 8.92 Feb-09 15.39 6.4 Mar-09 15.96 15.5 Apr-09 4.58 13.07 May-09 60.74 13.23 Jun-09 -3.36 4.25 Jul-09 24.2 14.84 Aug-09 -0.75 -4.61 Sep-09 22.94 10.47 Average 11.58 7.39 Std. Deviation 21.87 8.24
  21. 21. Chart Showing Monthly Returns
  22. 22. Spot Prices of Castor Oil (10 Kgs) Nov 2008 Oct 2009
  23. 23. Average Monthly Spot Prices of Castor Oil (10 Kgs) Months Rs. November-08 632.16 December-08 612.80 January-09 492.43 February-09 473.90 March-09 472.12 April-09 491.77 May-09 503.00 June-09 493.07 July-09 504.68 August-09 541.14 September-09 566.11 October-09 556.40
  24. 24. Average Monthly Spot Prices of Castor Oil (10 Kgs) Months Rs. Monthly Returns November-08 632.16 December-08 612.80 -3.06% January-09 492.43 -19.64% February-09 473.90 -3.76% March-09 472.12 -0.38% April-09 491.77 4.16% May-09 503.00 2.28% June-09 493.07 -1.97% July-09 504.68 2.35% August-09 541.14 7.22% September-09 566.11 4.61% October-09 556.40 -1.72% Avg. Returns -0.90%
  25. 25. Risk & Expected Rate of Return Expected return: is the weighted average of all possible returns multiplied by their respective probabilities R = expected return Ri = return for the i th possible outcome pi = probability associated with Ri n = no. of possible outcome R = ∑ pi Ri n i = 1
  26. 26. Variance • Variance of an asset’s return is the sum of the squared deviations of each possible rate of return from the expected rate of return multiplied by their probabilities • Variance (expected return) σ2 = Σ Pi (Ri – R)2
  27. 27. Illustration • Probability distribution of rate of return on stocks of Bharat Foods and Oriental shipping State of Probability of Rate of Return % Economy Occurrence Bharat Foods Oriental shipping Boom 0.30 25 40 Normal 0.50 20 10 Recession 0.20 15 -20 Bharat Foods R = 20.5% Oriental Shipping R = 13.0%
  28. 28. Risk of Expected Returns State of Economy pi Ri pi Ri Ri – R (Ri – R)2 pi(Ri–R)2 Boom 0.30 25 7.5 4.5 20.24 6.075 Normal 0.50 20 10.0 -0.5 0.25 0.125 Recession 0.20 15 3.0 -5.5 30.25 6.050 R = Σ pi Ri = 20.5 Σ pi (Ri – R)2 = 12.25 σ = [Σ pi (Ri – R)2 ]1/2 = (12.25)1/2 = 3.5% Expected returns of Bharat Foods’ Stock
  29. 29. Risk of Expected Returns State of Economy pi Ri pi Ri Ri – R (Ri – R)2 pi(Ri–R)2 Boom 0.30 40 12 27.0 729.0 218.7 Normal 0.50 10 5 -3.0 0.25 4.5 Recession 0.20 -20 -4 -33.0 1089.0 217.8 R = Σ pi Ri = 31.0 Σ pi (Ri – R)2 = 441.0 σ = [Σ pi (Ri – R)2 ]1/2 = (441.0)1/2 = 21.0% Expected returns of Oriental Shipping’s Stock
  30. 30. Why Standard Deviation (σ)? • Standard deviation is a measure of dispersion around the average (expected) value • Standard deviation considers every possible event and assigns equal weight to its probabilities • Easy to calculate, widely accepted
  31. 31. Certainty EquivalentCertainty Equivalent (CECE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Risk Attitudes
  32. 32. Certainty equivalent > Expected value Risk PreferenceRisk Preference Certainty equivalent = Expected value Risk IndifferenceRisk Indifference Certainty equivalent < Expected value Risk AversionRisk Aversion Most individuals are Risk AverseRisk Averse. Risk Attitudes
  33. 33. Portfolio • A portfolio refers to a group of assets owned by an investor • Assets in which an investor has made investments • Why Portfolio? – It is possible to construct a portfolio in such a way that the total risk of the portfolio is less than the sum of the risk of individual assets – To reduce risk, investors hold a diversified portfolio (equity capital, bonds, real estate, FDs, Bulion, etc.)
  34. 34. RP = Σ ( Wj )( Rj ) RP is the expected return for the portfolio, Wj is the weight (investment proportion) for the jth asset in the portfolio, Rj is the expected return of the jth asset, m is the total number of assets in the portfolio. m j=1 Portfolio (Expected) Return
  35. 35. Portfolio Risk: Standard Deviation • Standard deviation = √ variance • Variance of the portfolio (2-security case) σσ22 PP = ω= ω22 xxσσ22 xx + ω+ ω22 yyσσ22 yy +2ω+2ωxxωωyyσσxxσσyyCorCorxyxy
  36. 36. m j=1 m k=1 σσPP = Σ Σ Wj Wkσjk Wj is the weight for the jth asset in the portfolio, Wkis the weight for the kth asset in the portfolio, σjkis the covariance between returns for the jth and kth assets in the portfolio. Portfolio Risk: Standard Deviation
  37. 37. σσ jk = σ jσ k rr jk σjis the standard deviation of the jth asset in the portfolio, σkis the standard deviation of the kth asset in the portfolio, rjkis the correlation coefficient between the jth and kth assets in the portfolio. What is Covariance?
  38. 38. Portfolio Risk: Classification Systematic (non- diversifiable) • Market Risk • Inflation risk • Interest rate risk Non-Systematic (diversifiable) • Business Risk • Financial Risk
  39. 39. TotalTotal RiskRisk Unsystematic riskUnsystematic risk Systematic riskSystematic risk STDDEVOFPORTFOLIORETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors such as changes in nation’s economy, tax reform, Inflation or a change in the world situation. Total Risk = Systematic Risk + Unsystematic Risk
  40. 40. TotalTotal RiskRisk Unsystematic risk or DiversifiableUnsystematic risk or Diversifiable Systematic risk or Non-DiversifiableSystematic risk or Non-Diversifiable STDDEVOFPORTFOLIORETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors unique to a particular company or industry. For example, the death of a key executive or loss of a govt. contract. Total Risk = Systematic Risk + Unsystematic Risk
  41. 41. CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free raterisk-free rate plus a premiuma premium based on the systematic risksystematic risk of the security. Capital Asset Pricing Model (CAPM)
  42. 42. CAPM: Expected Return • The expected rate of return of a security: Expected return = Risk-free rate + Risk premium Risk premium =(Mkt return – Risk-free rate) x Beta Ri= Rf + (Rm – Rf) βi βi= COVim/ σ2 m Ri= αi + βiRm + εI(Characteristic Regression Line)
  43. 43. 1. Capital markets are efficient. 2. Homogeneous investor expectations over a given period. 3. Risk-freeRisk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). 4. Market portfolio contains only systematic risksystematic risk (use SENSEX or similar as a proxy). CAPM Assumptions
  44. 44. An index of systematic risksystematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The betabeta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. What is Beta?
  45. 45. Beta Calculation Beta = N ΣXY – (Σ X) (ΣY) N ΣX2 – (ΣX)2 Where X = return of market Y = return of stock

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