Inflation Indexed Bonds $\rho$ ₀ $\rho$ ₀ * I_t/I₀ $\rho$ At Any Time T

Inflation indexed bonds.
Many countries, among which the United Kingdom, the United States, and France, have issued inflation indexed bonds. Coupons and reimbursement value depend on the price index at the time of payment. Let's assume that a bond has been issued for 100 at time 0, with a maturity n and a real coupon equal to $\rho$ ₀ . Let I_t be the price index at time t. The coupon paid at t will be:
C_t= ^$\rho$ ₀ * I_t/I₀.
And the reimbursement value at maturity n will be:
R_n= 100 * I_n/I₀.
Since the reimbursement is also indexed on the price index, we can easily check that the actual yield is equal to the real coupon accrued by the inflation rate.
However, the real interest rate required by the market fluctuates with time. Knowing the market price of an inflation indexed bond and its real coupon, we can easily compute (using a discounting method) its real yield $\rho$ at any time t.
If the indexed bond still has n years to maturity, we just have to use the discounting method for a real cash-flow bond: $$P = \frac { \rho _ { 0 } } { ( 1 + \rho ) ^ { 1 } } + \frac { \rho _ { 0 } } { ( 1 + \rho ) ^ { 2 } } + \ldots + \frac { 100 + \rho _ { 0 } } { ( 1 + \rho ) ^ { n } }$$ Knowing the real interest rate $\rho$ we can compare it with the nominal interest rate r on classic bonds.
a. In terms of risk, what is the interest of such bonds? What kind of investors is it aimed at?
b. In terms of return, assume that yield curves r and $\rho$ are flat and that we expect the inflation level to remain constant for the coming years. You expect an annual inflation rate of $\pi$ . In what case do you prefer an inflation-indexed bond to a straight bond? [Find the relation between r, $\rho$ and $\pi$ ]