Mark's lecture 4 describes a famous "YC" carry trade strategy using T bonds. To keep things simple, we use zero bonds (coupon bonds same). Given a bond of 5Y maturity, next year's return is defined as the NAV 12M from now vs the current NAV. In other words, the ratio of next year's price over today's price. It's probably slightly above 1.0 or perhaps below 1.0.

This return factor is observable 365 days later, but we can predict it using the currently observable term spread, i.e. the 5Y yield - the 3M yield seen today.

Idea is, if the slope is steep, then we expect that return to be high. Steep slope basically means we observe high yield at the 5Y point on today's yield curve. Suppose it's a high 8.8%. If we were to hold the 5Y bond to maturity, we would realize approx. (without compounding) 44% return. Instead, we actually plan to sell the bond next year, so we are forecasting this bond price next year, effectively the 4Y point on next year's yield curve. (Apply P/Y conversion)

We expect that yield to remain around 8.8%, or equivalently, we expect the market yield on this same bond to remain. That would be higher than the riskfree rate (represented by the 1Y yield, say 0.8%).

However, If we are unlucky, the return factor (observable in a year) could come below the riskfree return factor today. (Note both deals cover the same loan period.)

* But then, we could cancel our plan and hold the bond to maturity and realize a total return of 44%. This is somewhat risky, because bond yield could rise further beyond 8.8%, hurting our NAV before maturity.

* Crucially, if the return over the next 12 months turns out to be lower than riskfree rate, then the subsequent 4 years must return more than 8.8% pa, since the return-till-maturity is fixed at 44%.

I have a spreadsheet illustrating that yield shifts in the next year may hurt the then NAV but the total return till maturity is unaffected.

However, If we are unlucky, the return factor (observable in a year) could come below the riskfree return factor today. (Note both deals cover the same loan period.)

* But then, we could cancel our plan and hold the bond to maturity and realize a total return of 44%. This is somewhat risky, because bond yield could rise further beyond 8.8%, hurting our NAV before maturity.

* Crucially, if the return over the next 12 months turns out to be lower than riskfree rate, then the subsequent 4 years must return more than 8.8% pa, since the return-till-maturity is fixed at 44%.

I have a spreadsheet illustrating that yield shifts in the next year may hurt the then NAV but the total return till maturity is unaffected.

EH (expectation hypothesis) actually says there's no reason to prefer the 5Y vs the riskfree rate. Contrary to EH, empirical data show that today's slope is a good predictor of the return over the next 12 months.

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