Is it zero?
My reference equation is:
Bi = σim / σm2
Is the top sigma of im considered to be zero, since treasury bills have a fixed payout? If not, how do you suggest calculating this value?
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Depends on how you define the bill's payout. If you are just considering cash flows the variance of returns will be zero. If you consider inflation adjusted cash flows (and apply the same logic to other risky assets and recompute the variance of market return) then you will obtain a non zero value.