I'm not worried about bonds. There is a saying, "a bad year for bonds is a bad day for stocks." When bonds have a bad year they are down in the 2-6% range. The worst year for bonds was -8%. Stocks on the other hand can drop 2-6% in a day and the worst year for stocks was -43%. You probably shouldn't decrease your bond allocation because you are worried about risk. The stocks are the risky part of the portfolio.
Bond investors have not seen a period of rising interest rates in decades.
From 2003 to 2006, slightly over 10 years ago, the fed funds rate went from <1% to over 5%. That's more than a 4% increase in 3 years.
VBTLX, Vanguard Total Bond index & VBLTX, Vanguard Long term bond index had positive returns every year during that period.
Now, you are right, the market value of the bonds went down as interest rates went up. However, the drop was so minor and spread over so many years that the income off the bonds covered the difference. Since the income is less now it would be easier for the returns to be negative, but it isn't anything to panic about.
Most ameteur bond investors have no idea that it's possible their 10 year bonds could drop 25-30% just because interest rates go up by 2%.
Just eyeballing duration these numbers don't appear possible. Yields are still positive, at least in the USA, so the duration on a 10 year bond mathematically has to be less than 10 years. That means if rates went up by 1% a 10 year bond would drop less than 10%, and if rates went up by 2% it would drop less than 20%.
I ran the numbers to check. For reference I used the TVM equation. Maturity = 10 years, semi-annual payments. Yield =2.2%. Rate increase = 1%. The market value of the bond drops 8.5%. Now add back in the 2.2% for a total return of -6.3%.
2% increase = -16.19% return. Add back the 2.2% for a total return of -13.99%
For context we are using 10 year treasuries in these examples. A well diversified bond portfolio, like VBTLX, has a lower maturity and lower duration so it would fair better. We are also talking about an increase of 2% within 1 year. Currently markets aren't sure if we are going to even see another 0.25% by the end of the year.
But what about when there isn't much room for bond yields to fall?
Bond yields can still fall. When there is uncertainty people will gladly pay for safety. When the UK voted to leave the EU stocks in Europe dropped at the same time government bond yields in the EU dropped which pushed bond prices up. Bonds went up when stocks went down. Keep in mind that interest rates on many of those bonds were already negative. Investors were happy to pay Germany for the safety of their bonds in a world that had just become more uncertain. US bonds still have positive yields so we aren't even in that situation yet. Now, during the 08 crash there was a day when short term treasuries were selling with negative yields on the secondary market. Investors were panicking, they wanted something safe, and the money was moving so quick people probably didn't even realize the yield was negative. When panic sets in people want safety. Under normal circumstances that safety means you have a return that is lower than inflation, a negative real return. Now we have low inflation so the negative return is more obvious, but it was always there.
Conclusion: don't panic over bonds. They are a hedge against stocks that also given you some income along the way.