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How to calculate the bond price from the yield for 10 Year Treasuries?

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Hi Cullen,

So I’m using historical bond yield data of US 10 year treasuries all the way back to 1871 from this cool site: https://www.multpl.com/10-year-treasury-rate/table/by-year

I calculated the bond price by inverting the yield (1/yield) and indexing the price to 100 on 1871.

This is what I get for my estimation of the bond prices (see attached graph).

However I’m not sure if this is the right approach because from 1941 – 1982 it shows that bond prices crashed by -87%. Whereas in reality the maximum historical decline in bond prices was about -20 to -30%, a figure I think I read in one of your articles and elsewhere.

So what am I missing here? How is the 10 year bond price supposed to be estimated from the yield? I know you probably need the coupon rate and maturity dates for an accurate calculation. But for a rough back-of-the-hand calculation with just yield data, what is the correct approach to calculate the price for 10 year treasuries?

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    Posted by Incognito 7
    Posted on 04/14/2017 6:12 AM
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    That -87% decline is in real terms. Which, honestly, is a stupid way to judge bonds. Bonds are not designed to beat inflation so the real return is an incorrect benchmark. Even TIPS are just designed to match inflation. So this whole idea of comparing bonds to inflation is misleading IMO.

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    Cullen Roche Posted by Cullen Roche
    Answered on 04/23/2017 11:29 AM
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      Sorry I don’t follow. I’m not comparing bonds to inflation here. Just asking whats a reasonable method of calculating the bond price from the bond yield? Or is that not possible with the given information?

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      Posted by Incognito 7
      Answered on 04/24/2017 4:21 AM
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        @Incognito7: Roche’s off his rocker again! 🙂 But that’s not how you calculate constant maturity bond prices. Use this formula for monthly yields (available at FRED) to generate a total return time series :

        currentPrice = previousPrice * (((((previousRate * (1 – (1 + currentRate) ^ (maturityYears * -1)) / currentRate) + (1 / (1 + currentRate) ^ maturityYears) – 1)) + (average(previousRate, currentRate) / 12)) + 1)

        @Roche If bonds aren’t designed to beat inflation, what the heck are they for then? Because in the long-term, they do beat inflation just as stocks, bills and gold do. Only literal currency and coins held under the mattress do not. The long-term is …. really long.

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        Posted by MachineGhost
        Answered on 04/25/2017 5:46 PM
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          @ Incognito,

          Sorry for the slow response. This one slipped through the cracks.

          I would just use a bond price calculator. There are a million of them online. The math here is too complex to write out and do on your own when there are so many good resources that simplify this stuff.

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          Cullen Roche Posted by Cullen Roche
          Answered on 04/25/2017 6:16 PM
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            @ MG,

            Bonds typically pay about the rate of inflation. They won’t really beat inflation, but will only maintain your purchasing power. That’s not why you should own bonds though. You own bonds because they are a very inexpensive way of hedging your equity market risk.

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            Cullen Roche Posted by Cullen Roche
            Answered on 04/25/2017 6:17 PM
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              @Roche: I’d figured you would say something like that. But lets go back in time before the 1960’s and mainframes. Was it common wisdom then that you should own bonds in a portfolio for hedging your equity market risk? Did Graham mention anything?

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              Posted by MachineGhost
              Answered on 04/25/2017 7:52 PM
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