R. 49 Economics and Investment Markets

Question 1

Inter-temporal rate of substitution (ITRS)

• definition
• inverse relationships
• relationship to expected future price of risk asset

Answer 1

Inter-temporal rate of substitution (ITRS)

• Ratio of the marginal utility of consumption in the future to the marginal utility of consumption today.

Inverse relationships

• real GDP growth
• one-period real risk-free rate

ITRS and E(P) of risk asset

• Negative Covariance bw ITRS and expected future price of a risky asset, which results in a positive risk premium.
• Larger negative covariances have higher risk premiums
• Note that with a one-period default-free bond, the covariance term is zero because the future price is a known constant ($1). Covariance of a random quantity with a constant value is always zero.

Question 2

Real default-free interest rate relationships

Nominal short-term rate calc

Nominal long-term calc

Answer 2

Real risk free (RF) rates are positively related to:

• GDP growth rate.
• Expected volatility of GDP growth.

Nominal short-term r = Real_RF + π

• where π = expected inflation ​​

Nominal long-term r = Real_{RF +} π + ϴ

• where ϴ = uncertainty of inflation

Question 3

Taylor rule for short-term interest rates

Answer 3

Taylor Rule says policy rates are positively correlated with:

1. Level of real short-term interest rates
2. Excess of Inflation less Target inflation
3. Excess of Actual real GDP less Potential real GDP
   
   • called “output gap”

Question 4

Break-even inflation (BEI) rate

BEI _{longer maturity bonds}

Credit risky bonds

Equity

Commercial real-estate

Answer 4

a

Break-even inflation rate: difference between yield on a zero-coupon default-free nominal bond and the yield on a zero-coupon default-free real bond (includes expected inflation and risk premium for uncertainty over future inflation)

BEI = (Nominal Yield_{Risk-Free Zero CPN Bond}) - (Real Yield_{Equivilant Bond} )

BEI for longer maturity bonds = π + ϴ

where:

π = expected inflation

ϴ = risk premium for uncertainty about actual in nation

Credit risky bonds_{required rate of return} = R + π + ϴ + y

where:
R = Real risk-free rate

y = additional risk premium for credit risk = credit spread

Equity_{<strong>Discount rate</strong>} = R + π + ϴ + y + K

where:
K = risk premium relative to risky debt for investment in equities
equily risk premium = y + K

Commercial real estate_{Discount rate} = R + π + ϴ + y + K + Ψ
where:
K = risk premium for uncertainty of terminal value of property
Ψ = risk premium for illiquidity