I still want to see the math. Yes, a bond will lose market value when interest rates are rising. But that bond also creeps towards maturity year over year, causing its price to converge towards its face value regardless of rate environment; and new units purchased at that point go in at the higher yield. In a bond fund, the higher-duration bonds will tick down over those years and converge towards their own face values.
There's a huge difference between bond prices that drop because of interest rates, and share prices of AIG/Citigroup/GE that drop due to investor confidence. Shares of those companies have no underlying redemption value. Bonds do, regardless of the market prices they encounter along the way, and duration is what measures how far their market prices will deviate. If I hold a 20-year government bond and the market value drops 20% due to a rise in interest rates, it doesn't mean there's a risk the bond will go bankrupt. I will still collect all the payment and recoup the face value if I hold it to maturity.
The math is simple, in Canadian market context; there is a practically complete cycle of rising interest rate of environment of 31 years from 1950 to 1981 and a falling interest rate environment of 29 years from 1981 to 2010, though both the rise and fall are not straight line.
So if we [assume we were investing adult then] were to go back to 1950, if you were to invest in 20 year bond [assuming there is 20 yr bond] in a rising interest rate environment for the next 31 years. For performance basis comparison made between  Stocks,  Bonds,  GICs,  Inflation. Let me first talked about inflation, if we are comparing all the 4 comparing investing classes assuming inflation is an investing class for comparison purpose. If all the investing asset class were to have initial $100 investment and reinvest the 'yield' returns similar to DRIP used in stocks. For comparison for the next 31 years along the way taking 5, 10, 15, 20, 25, 30 yr, readings of MARKET VALUES of each asset class; the actual case in history [from memory] is that bonds mostly can not even beat inflation because of capital losses along the way and GICs performed better because there is no capital loss at any point in market value of holdings and also beating inflation. Stocks as investment class was a runaway success story.
Of course, in a falling interest rate environment, bonds will most likely be a runaway success story because of capital gains plus starting with a very high bond yield. But to start from a very low interest rate environment, for rising rate over a prolonged period:
1. Ask yourself, do you have the stomach to see that your bond investment is underwater compare to inflation?
2. There may also be some point in time that you stock holdings go for a tail spin when you bond holdings are also in the dog house.
For the historic comparison as in Andex Chart, long bond is used for comparison. Even if one were to use ladder bonds, in a prolonged period of rising rates environment, the market value at any point in time will still be below that of GICs. But when long bond is used, because of the compounding effect, the stocks outperformed bonds by a HUGE margin in dollar value.