# 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 thinkâ€¦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 confusingâ€¦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: itâ€™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 itâ€™s greater than 1, you need a couple more futures contracts to match the yield change on the portfolio; if itâ€™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 itâ€™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