Asset Price Basic Equations

1. Equity Price
q(t)=βE[u'(c(t+1))(q(t+1)+x(t+1))]/u'(c(t))

2. Risk Free Bond Price
p1(t)=βE[u'(c(t+1))]/u'(c(t))

3. Two-Period Bond Price
p2(t)=β^2E[u'(c(t+2))]/u'(c(t))

4. One-Period Forward Contract Price
pf(t)=βE[u'(c(t+2))]/E[u'(c(t+1))]

5. Equity Premium
EP(t)=E[q(t+1)+x(t+1)]/q(t)-1/p1(t)

6. Term Premium
TP(t)=E[p1(t+1)]/p2(t)-1/p1(t)

These equations are derived from the following DP:

State Variables:  e(t-1) b1(t-1) b2(t-1) f(t-1) f(t-2) x(t)
Control Variables: c(t) e(t) b1(t) b2(t) f(t)

V(e(t-1) b1(t-1) b2(t-1) f(t-1) f(t-2) x(t))
  =max{u(c(t))+βEV(e(t) b1(t) b2(t) f(t) f(t-1) x(t+1))
           +λ(t)[(q(t)+x(t))e(t-1)+b1(t-1)+p1(t)b2(t-1)+f(t-2)
                     -c(t)-q(t)e(t)-p1(t)b1(t)-p2(t)b2(t)-pf(t-1)f(t-1)]}

If the endowment (x) is distributed as i.i.d,
(i)  equity, risk free bond and two-period bond prices are positively correlated with the (current) endowment, and
(ii) the price of the one-period forward contract is constant,
on the ground that
(i)  the numerators in the three prices are constant (i.i.d. expected values) and the denominators are increasing in the endowment, while
(ii) both the numerator and denominator of the one-period forward contract price are expected values.

Equity Premium

sign[EP]=-sign[cov(u'(c(t+1)),q(t+1)+x(t+1))]

Abel (1999) "Risk premia and term premia in general equilibrium"
In the standard Lucas fruit-tree model, the risk premium is necessarily positive.
http://www.sciencedirect.com/science/article/pii/S0304393298000397

Term Premium

sign[TP]=-sign[cov(u'(c(t+1)),p1(t+1))]

If the endowment (x) has positive serial correlation, then the sign of the term premium is indeterminate; in other words, the sign can be negative.

If the endowment (x) has negative or no serial correlation, then the sign of the term premium is positive.

http://www2.wiwi.hu-berlin.de/wpol/html/asset/pdf/lec02_LucasAssetPricing.pdf