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So much in the news about inflation, and interest appreciation dooming long-term bond funds. Are short-term bond funds affected by the same risk? Does this make investing a portion of your portfolio into a bond allocation not wise?

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Yes, but the magnitude of the risk impact, varies very differently for short term bonds than long term bonds. Look at it intuitively and you may get an idea. What you will get tomorrow is going to be more certain than what you may get maybe a year later. For a long term bond, your payment is distributed over a large period of time, that gives it more exposure to the volatility in the market and your payment of principal is a long way off. So forgoing your payment for a longer time, makes you demand a higher yield rate from a long term bond than a short term bond. Hence the lower price of a long term bond.You are more exposed to the interest rate changes in the market so you carry a higher interest rate risk on a long term bond than a short term bond.

Regarding inflation risk, try a inflation bond which takes care of the inflation risk. Inflation risk also has a effect on the payouts of bonds. Some pointers on inflation risk

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