Suppose the real yield of a one$-$year inflation protected discount bond is $-1\%$ and the nominal yield of a one$-$year nominal discount bond is $3\%.$ Consider the following investment strategies:

Short $$1M$ worth of inflation$-$protected bonds $($you effectively borrow at the real yield$)$ and use the proceeds to buy $$1M$ worth of nominal bonds.

Short $$1M$ worth of nominal bonds $($you effectively borrow at the nominal yield$)$ and use the proceeds to buy $$1M$ worth of inflation$-$protected bonds.

You can ignore any margin requirements for this question.

$($a$)$ What is the break even inflation rate?

$($b$)$ Suppose investor A thinks that expected inflation is going to be $6\%.$

$($i$)$ What is her perceived inflation risk premium?

$($ii$)$ Given her beliefs about inflation, which investment strategy do you recommend?

$($iii$)$ Suppose she follows your investment advice and it turns out that realized inflation rate is as she expected. What is her profit$/$loss$?$

$($iv$)$ Suppose she follows your investment advice and the realized inflation rate is $2\%.$ What is her profit$/$loss$?$

$($c$)$ Suppose investor B thinks that expected inflation is going to be $2\%.$

$($i$)$ What is his perceived inflation risk premium?

$($ii$)$ Given his beliefs about inflation, which investment strategy do you recommend?

$($iii$)$ Suppose he follows your investment advice and it turns out that realized inflation rate is as he expected. What is his profit$/$loss$?$

$($iv$)$ Suppose he follows your investment advice and the realized inflation rate is $6\%.$ What is the profit$/$loss$?$