Risk and Return

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Risk and Return
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Risk and Return

• Various Ways to Discount Cash Flows
• - WACC
• - APV
• - FTE
• We shall see these in action shortly
• But First
• What is the WACC

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Risk and ReturnWACC, A Simple Example

• A Company wishes to finance a project with 70
  Equity and 30 Debt
• Total needed GBP 50,000,000
• Tax rate 30
• Cost of Equity 12
• Cost of Debt 7

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Risk and ReturnWACC, A Simple Example

• So
• WACC
• Equity bit 35,000,000 x 12 8.4
• 50,000,000
• Debt bit 15,000,000 x (1 - .3) 1.47
• 50,000,000
• WACC
  9.87

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Risk and Return

• But, A Few Quick Questions
• How do we get the cost of debt?
• Easy, ask a bank
• (We will return to the 1-t issue)
• How do we get the cost of equity?
• A bit trickier

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Risk and ReturnCost of Equity

• Rational Economic Person
• Risk is not bad but greater risk, greater
  expected return
• Risk Measurements
• Expected return
• Variance
• Standard deviation

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Risk and ReturnCost of Equity

• Returns Deviation from Mean Deviation
  Squared 3
  (9)
  81
• 4 (8)
  64
• 33 21
  441
• (6) (18)
  324
• 10 (2)
  4
• 21 9
  81
• 4 (8)
  64
• 12 0
  0
• 15 3
  9
• 12 0
  0
• 120
  1068
• Mean 12
  Var 118.7 1068/n-1
• 
  SD 10.89

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Risk and ReturnCost of Equity

• Assuming a normal distribution
• Range Probability Downside risk
• Within
• / - 1 SD 66.67 16.67
• / - 2 SD 95.00 2.5
• / - 3 SD 99.75
  .125
• Share has Av return of 14
• SD of 4
• Need min return of 8, with only 2.5 chance of
  less
• Do we invest?
• No as 2.5 2 SD 8 and 14 -8 6

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Risk and ReturnCost of Equity

• Risk changes in a portfolio( 2 or more
  assets)
• Expected Return of a portfolio
• Weighted average of the assets in a portfolio
• E.g. Asset A, ER 8, 30 of portfolio
• Asset B, ER 12 70 of portfolio
• Portfolio ER 8 x .3 12 x .7 10.8

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Risk and ReturnCost of Equity

• But what about the risk of a portfolio?
• What happens when we put assets together that
  react differently to overall market movements?

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Variance of a Portfolio

• But what is the variance?

Umbrellas
ER
Cider
ER
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Risk and ReturnCost of Equity

• We may have a range of portfolios of differing
  expected returns and risks
• There is a risk free asset, Government stocks
  (Gilts - Bills and Bonds)
• Capital Market line
• Market Portfolio

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Risk and ReturnCost of Equity

• But how to price an individual asset?
• How does the risk of the individual asset vary
  from that of the Market Portfolio?
• Risk split into
• Market risk systematic non-diversifiable
  
• 
  risk
• Specific risk unsystematic diversifiable risk

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Risk and ReturnCost of Equity

• Since diversifiable risk may be diversified away
  just left to focus on
• Market Risk
• Some shares riskier than others
• Measure of relative risk is
• Beta
• Beta Covariance of the Market and Asset
• Variance of the Market

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Variance of a Portfolio

• The riskiness of an asset held in a portfolio is
  different from that of an asset held on its own
• Variance can be found using the following formula
• Var Rp w2Var(RA) 2w(1-w)Cov(RARB)(1-w)2VarRB
  
• Cov stands for Covariance
• Covariance is a measure of how random variables,
  A B move away from their means at the same time

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Risk and ReturnCost of Equity

• Required return (or expected return)
• ERA RF (ERM RF)B
• Example
• Company A Beta of 1.4, Risk Free 5
• Expected return on market 10
• ERA 5 (10 -5) 1.4 12

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CAPM

• Security Market Line
• Rm Market
  Portfolio
• Rf
• 0 1.0
  2.0 Beta

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Risk and ReturnCost of Equity

• Other models
• Gordon Dividend Growth
• ER D1 g
• P0
• E.g. Share price 275 pence
• Current Div 8.25 pence
• Historic growth 9
• 8.99 .09 12.27
• 275
• Arbitrage Pricing Theory. Not going to bother but
  

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Fama-French3 Factor Model

• To estimate the expected returns under APT
• Expected risk premium, r - rf
  b1 (rfactor1-rf) b2(r factor2
  -rf) b3 (r factor3 -rf) etc etc
• So all we have to do is
• Step 1. Identify a reasonably short list of
  macroeconomic factors that could affect stock
  returns
• Step 2. Estimate the expected risk premium on
  each of these factors
• Step 3. Measure the sensitivity of each stock to
  the factors

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Fama-French3 Factor Model

• Above average returns on
• Small sized companies and
• High book to market value
• R rf bmarket(rmarket factor)bsize(rsize
  factor) bbook too market(rbook to market factor)

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Fama-French3 Factor Model

• Having worked out from market data that
• Market premium 7
• Size premium 3.7
• Book to market premium 5.2
• Then for
• E.g. computers bmkt 1.67, bsz .39 and bmkt to
  bk -1.07
• ER (1.67x7)(.39 x 3.7) (-1.07x5.2)
• 7.6 Rf

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Risk and ReturnCost of Equity

• Any problems?
• Market returns/Market risk premium
• It varies from
• - market to market
• - period to period
• - arithmetic or geometric
• So anywhere between 0 and 10!!

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Risk and ReturnCost of Equity

• Real WACC
• Should always use market values for Equity and
  Book values are used for debt (relevant for
  leverage discussions)
• WACC we work out will probably be nominal cost
  of capital. Suppose we want the real cost of
  capital?

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Risk and ReturnCost of Equity

• Say WACC 9.87 and inflation is 3
• Then the real WACC is
• 1 nominal wacc - 1
• 1 inflation rate
• 1.0987 1.061 1 .061 or 6.1
• 1.03

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Risk and ReturnCost of Equity

• Lastly the 1 t issue.
• Because interest on debt is allowed as an expense
  before tax the government subsidises the cost of
  debt.
• EBIT 5,000 5,000
• Int 120
  _____
• EBT 4,880 5,000
• Tax _at_ 40 1,952 2,000
• Net 2,928 3,000
• Tot returns 3,048 3,000
• Dif 120 x .4 48