# Yield beta

Whats the significance of yield beta?

the duration tells you the percent change in the price of the bond for a 100 bps change in the yield.

So assume you have a bond priced at 100 with a duration of 10, and you want to use of future to hedge it with a price of 100, and a duration of 5.

You would think to use the formula:

Nf = (0-10)*(100/100) / 5 = 2

You might think…oh, it has half the duration soyou would need two futures contracts to hedge this bond (as athe above formula would suggest).

HOWEVER, that is only the case of a 100 bps change in the bond is matched by a 100 bps change in the bond underlying the future.

So if beta = 0.5, that means that a 1bps change in the interest rate undedrlying the future will correspond with a 0.5 bps changein the interst rate of the bond to be hedged. So you actually only need 0.5x the amount of futures:

NF = (0-10)*(100/100)*(0.5) / 5 = 1

Sorry if that is confusing…basically beta not equal to one suggests that when the yield on the bond underlying the futures changes by 100 bps, the bond to be hedged changes by (beta)*100 bps.

Same as any other beta: it’s the slope of a regression line.

In this case, you plot the returns on the underlying bond (or bond portfolio) against the returns on the futures; the slope of the regression line is the yield beta. If it’s greater than 1, you need a couple more futures contracts to match the yield change on the portfolio; if it’s less than 1, you need a couple fewer futures contracts.

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FYI, this is not accurate. A duration of 10 gives you the expected % change for a 100bps change in interest rates, by definition, assuming no convexity. If rates rise 1%, price should fall by 10%. Straight out of the text.

Obviously it’s just a matter of dividing by 100 for your answer to be accurate, but when somebody says the duration is 10, they mean what I wrote above.

this is true. thanks for catching that