JAN MOSSIN 3. RISK MARGINS The expected rate of return r, on a unit of a risky asset can be def u/(1+ri)=Pi, i.e., r;=(/pi)-1,(=l,,n-1). Similarly, the rate of return of a unit of the riskless asset rn is defined by 1/ (1+rm=g, i.e, rn=1 g-1. with our earlier interpretation of the riskless asset in mind, rn may be regarded as the pure rate of interest. The natural definition of the pure rate of interest is the rate of return on a riskless asset. In general, we may think of the rate of return of any asset as separated into two parts: the pure rate of interest representing the "price for waiting, and a remainder, a risk margin, representing of risk”Whe yield of the riskless asset at I and decided to fix its current price at g, we thereby implicitly fixed the pure rate of interest. And to say that the market determines only lative asset prices is seen to be equivalent to saying that the pure rate of interest is not determined in the market for risky assets. Alternatively, we may say that the asset market determines only the risk margins. The risk margin on asset j, mi, is defined by =-1n=-D/q To compare the risk margins of two assets j and k, we write m=此一PqD nk We now make use of the equilibrium conditions. From (5)we have ∑nx21∑xx2 Summing over i and using(7), we then get 4j-Pjiq Fk-pk/q These equations define relationships between the prices of the risky assets in terms of given parameters only. We can then write Pkk k∑如又Px Now, ijEajaia is the variance of yield on the total outstanding stock of asset j <-, is similarly the total value, at market prices, of all of asset j. Let us denote n.se magnitudes by V, and R;, respectively. In equilibrium, therefore, the risk reins satisfy has content downl ued stube to sT oR ems aecondtp23013020-0 AM774 JAN MOSSIN 3. RISK MARGINS The expected rate of return rj on a unit of a risky asset can be defined by ,uj/(l +rj)=pj, i.e., rj=( pjlpj)- 1, (j= l, ..., n- 1). Similarly, the rate of return of a unit of the riskless asset rn is defined by 1/(1 +rn)=q, i.e., rn= l/q- 1. With our earlier interpretation of the riskless asset in mind, rn may be regarded as the pure rate of interest. The natural definition of the pure rate of interest is the rate of return on a riskless asset. In general, we may think of the rate of return of any asset as separated into two parts: the pure rate of interest representing the "price for waiting," and a remainder, a risk margin, representing the "price of risk." When we set the future yield of the riskless asset at 1 and decided to fix its current price at q, we thereby implicitly fixed the pure rate of interest. And to say that the market determines only relative asset prices is seen to be equivalent to saying that the pure rate of interest is not determined in the market for risky assets. Alternatively, we may say that the asset market determines only the risk margins. The risk margin on asset], in, is defined by mj = rj- r =t Hi pjlq Pj To compare the risk margins of two assets j and k, we write: mj - __ _ lj- __ pjlq _P Pk Ink Pk Pklq P j We now make use of the equilibrium conditions. From (5) we have: >3 Ef YCX~ aa Zik,X E Uko, Xa (9) q (j,k=1,... ,n-1). pj - pjlq 1-k Pklq Summing over i and using (7), we then get: A, ufjxa Xa ,U ka XaT (10) a a yUj p;lq Ilk Pklq These equations define relationships between the prices of the risky assets in terms of given parameters only. We can then write: m i _ _ _ _ _ _ _ mj Xj ,> . fja 5Xa __ _ _ x cx Pk Xk4 Mk Xk54 Eka Xa Pj Xj Now, x; jc is the variance of yield on the total outstanding stock of asset j; pjxj is slmilarly the total value, at market prices, of all of asset j. Let us denote these magnitudes by Vj and Rj, respectively. In equilibrium, therefore, the risk margins satisfy: This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:20:50 AM All use subject to JSTOR Terms and Conditions