Risk Premium

Risk Premium. 오래 전에 썼던 'Basic of Fixed Income Basic (1)'에서 이어지는 내용입니다. 하지만 제목 없이 쓰다보니 주제는 Fixed Income이 아니라 risk premium이 되었습니다. 원래 영어로 썼던 내용. 다시 한글로 옮기려니 시간이 없어서 이번에도 그냥 영문으로 올립니다.

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2. Fixed Income Risk Premium

E(r) = real interest rate + inflation risk premium + default risk premium + liquidity risk premium + maturity premium

 

(1) Real (risk-free) interest rate

   ▪ A single interest rate for a completely risk-free securities if no inflation were expected

   ▪ The time preference for the current vs future real consumption

   ▪ Future Value = Present Value + tan(Θ) = Present Value * (1+R)

 

(2) Inflation risk premium

   ▪ Compensation for expected inflation

   ▪ Norminal interest rate(r) = real interest rate(R) + inflation rate(i)

     ◦ interest rate of short term government note

 

(3) Default risk premium

   ▪ Compensation for the possibility that the borrower can not make a promised payment

(4) Maturity premium

   ▪ YTM of long term liquid government bond - YTM of short term liquid government note

(5) Liquidity risk premium

   ▪ Compensation for the loss to be converted to cash

   ▪ Risk that can not be converted to cash when it is needed

   ▪ It become more important right after financial crisis because most of financial crisis is linked with liquidity problem

(6) Option premium

   ▪ + Call option premium - Put option premium

It's not easy to devide the risk premium in practice, but it's helpful to understand the natures of risk premium.

3. Equity Risk Premium

E(r) = Norminal interest rate + Equity risk premium

   ▪ Norminal interest rate = YTM on Long term bond

(1) Historical method

   ▪ Equity risk premium from historical data

(2) CAPM

   ▪ Risk premium(rpi) = β * (E(rm) - rf)

   ▪ β = cov(ri, rm) / var(rm) = (σi/σm) * ρim * rpm

        = σi * ρim * (rpm/σm) = σi * ρim * sharpe ratio of market(SRm)

(3) ICAPM (Singer-Terharr)

   ▪ fully intergrated = σi * ρim * SRm

   ▪ fully segmented = σi * SRm

   ▪ d = the dregree of intergration

   ▪ rpi = σi * ρim * SRm * d + σi * SRm * (1-d)

(4) Survey Method

   ▪ To ask experts for their expectation