Equity Valuation: Return Concepts

Question 1

Holding Period Return

Answer 1

r = [(Dh + Ph) / Po] -1

1. Dh: Dividend
2. Ph: Price at end of holding period
3. Po: Price at beginning of holding period

Question 2

Expected Return Components (2)

Answer 2

1. Required return
2. Return from convergence of price to value (mispricing between Vo and Po or “Alpha”)

Question 3

Return from Convergence of Price to Value

Answer 3

1. Second component of return
2. (Vo - Po) / Po

Vo: Intrinsic value (analyst estimate)

Po: Price in the market

Question 4

Convert Annual Holding Period Return to Semi-annual

Answer 4

Semiannual HPr = [(1 + HPr)^1/2] - 1

This can then be done to convert any HPr to whatever period you want.

Question 5

Convert Annual HPr to Total Return over X Years
Then Annualize that Return

Answer 5

HPr (over x years) = [(1 + HPr)^X] -1

HPr annual = [(1 + HPr over x years)^1/x] -1

Question 6

Internal Rate of Return (Intrinsic Value)

Answer 6

Vo = D1 / (Ko - G)

• Ko: Required return
• D1: Dividend next year
• G: Growth rate of Dividend

Question 7

Internal Rate of Return (Required Return)

Answer 7

Ko = (D1 / PmkT) + G

• assumes PmkT is = IV (efficient market)

Question 8

Convert ROE to a Dividend Growth Rate (G)

Answer 8

G = ROE X (1-PayOut)

Question 9

Equity Risk Premium - Market

Individual Public Stock Required Return (ERP)

Individual Private Stock Required Return (ERP)

Answer 9

3 is a buildup method

1. ERP = RoE(MrkT) - Rf%
2. Ri = Rf% + β(ERP)
3. Ri(private) = Rf% + ERP(MrkT) +- other risks or premiums appropriate for i

Question 10

Beta

Answer 10

β = CovMrkT / VarMrkT

Question 11

Historical Estimates for ERP

Answer 11

Average difference between Rf% and market returns

• • tends to be counter-cyclical*
• • Subject to survivorship bias*
• • geometric vs. arithmetic?*

Question 12

Forward Looking Estimates for ERP (GGM)

Answer 12

ERP (GGM) = (D1/Po) + G - Rf%

-Gordon growth model must rely on developed markets

Question 13

Macroeconomic / Supply-Side Model (ERP)
Ibbotson Chen Model

Answer 13

ERP = {[(1+EInfL)(1+EGrEPS)(1+EGPE) - 1] + EinC} - ERf%

• • EInfL: Expected inflation (Δbetween Treasury Bonds and TIPS)*
• • EGrepS: Growth in EPS (or Growth in GDP)*
• • EGpE: Growth in PE (Expected increases or decreases of market is overvalued)*
• • EinC: Growth in income (can be market yield)*

Question 14

Multifactor Models

1. Required Return
2. Risk Premium

Answer 14

Required Return = Rf% + (risk premium) + (risk premium2) + …

Risk Premium = (Factor sensitivity X Factor Risk Premium)

• factor sensitivity = factor β

Question 15

Fama - French Model

Answer 15

Ri = Rf% + βi(mrktRMRF) + βi(sizeSMB) + βi(valueHMI)

• • RMRF: Market Risk Premium*
• • SMB: Small cap return Premium*
• • HML: Value return premium (*
• • Explains why small cap stocks have a higher return than CAPM would predict?*

Question 16

Pastor Stambaugh Model (PSM) to determine Ri

Answer 16

Ri = Rf% + βi(mrktRMRF) + βi(sizeSMB) + βi(valueHMI) + β(liqLIQ)

• • RMRF: Market Risk Premium*
• • SMB: Small cap return Premium*
• • HML: Value return premium*
• • LIQ: Liquidity*
• • Explains why small cap stocks have a higher return than CAPM would predict?*

Question 17

Five Factor BIRR Model (macroeconomic model)
CTYIBM

Answer 17

- Economic _not _ Fundamental factors

1. Confidence risk: unexpected Δ in Δ of Jnk and govt bonds
2. Time horizon risk: unexpected Δin Δ of R% on 2-yr and 30-d gvt bonds
3. Inflation risk: unexpected Δ in inflation
4. Business cycle risk: Unexpected Δ in business activity
5. Market timing risk: % of total return on MrkT not explained by first 4 factors.

59:16

Question 18

Blume Adjusted Beta

Answer 18

Adjusted β = (2/3)(β) + (1/3)(1)

Question 19

Unlevering Beta and then Relevering Beta for Comparisons

Answer 19

1. βᵤ = ( 1 / 1+DE )βₑ
2. βₑ = (1 + DE)βᵤ