# Retiree’s glass half full when interest rates rise

Since the early eighties interest rates have been on a general descent, with a few small variations along the way. For anyone who purchased annuities years ago, or owned longer term bonds, the returns were much higher than today. In July 2012, the Government of Canada 30 year bond rate fell to 2.2 per cent – a historic low. We are beginning to see longer term interest rates beginning to climb from these historic lows. One question I have been asked many times is why existing bonds decline in value when interest rates rise, and vice versa. This inverse relationship is confusing for investors not familiar with bonds.

To illustrate this inverse relationship we will use two 30 year Government of Canada bonds with a face value of $100,000. Let’s assume Bond A was issued one year ago with a coupon rate of 2.20 per cent, and Bond B was issued today with a coupon rate of 2.95 per cent. Unlike common equities, once the coupon of a bond is set it does not change. When bonds are initially issued they have a par value of 100 and will mature at 100 par value. Throughout the life of a bond it will trade at either at a discount (below 100) or at a premium (above 100). All else being equal, if current market rates are higher than the bond’s coupon, it will trade at a discount. If current market rates are lower than the bond’s coupon, it will trade at a premium.

Going through the calculations will also help with understanding the inverse relationship of bonds. Bond A pays income of $2,200 per year. For a 30 year bond, this equals $66,000 (30 x $2,200) in total income during the full term. Bond B pays income of $2,950 per year. For a 30 year bond, this equals $88,500 (30 x $2,950) in total income. Bond B will pay $22,500 more in interest than Bond A ($88,500-$66,000). In order for someone to sell Bond A today they would have to accept a price of 77.50 par value, or 77,500. The second buyer of Bond A would purchase the bond for $77,500 then receive $100,000 at the end of the 30 years. The second buyer of Bond A would have a capital gain of $22,500 plus interest income of $66,000 which would equal the $88,500 in interest income that the holder of Bond B receives. These calculations are overly simplistic and do not factor in the time value of money or taxation items, both of which are important concepts in bond valuations. The time value of money is the notion that a dollar today is worth more than a dollar tomorrow. The calculations above would be different if these items were factored in.

The number of years that a bond has before it matures may be referred to as “term” or “duration”. The longer the duration of a bond, the more it will fluctuate in value if interest rates change. Let’s use Bond A and B again but assume that the term is ten years and not 30. Bond A pays income of $2,200 per year. For a ten year bond, this equals $22,000 (10 x $2,200) in total income during the full term. Bond B pays income of $2,950 per year. For a ten year bond, this equals $29,500 (10 x $2,950) in total income. Bond B will pay $7,500 more in interest than Bond A ($29,500-$22,000). In order for someone to sell Bond A today they would have to except a price of 92.50 par value, or 92,500. The second buyer of Bond A would purchase the bond for $92,500 then receive $100,000 at the end of the ten years. The second buyer of Bond A would have a capital gain of $7,500 plus interest income of $22,000 which would equal the $29,500 interest income that the holder of Bond B receives.

The loss on the value of Bond A incurred in the ten year example is $7,500 after one year, which is significantly lower than the $22,500 loss on the 30 year bond. Investor A only lost $5,300 if the interest income of $2,200 received in the first year is factored in. When investors feel that interest rates may rise, one strategy is to execute a switch trade and simultaneously sell longer term bonds, and purchase shorter term bonds. The downside to this strategy is that short term bonds have lower current yields and rates may not rise. Investors shifting to shorter term bonds will sacrifice a lower yield today to lessen the risk of an even larger decline in value of the bonds if interest rates rise.

Much attention has been placed on the negative impact on existing bonds if rates rise. If we flip the conversation and discuss the benefits for investors – the glass is half full when rates rise. To illustrate we will use a recently retired investor named Charlie who has a corporate bond portfolio valued at $500,000 today and is yielding 3.5 per cent. Annually Charlie is currently earning interest income of $17,500. If interest rates rise to the point where Charlie can earn 5.0 per cent on his corporate bonds then Charlie is clearly a winner in the long run as his annual income jumps up to $25,000. For Charlie to benefit in the long run with rates rising it is important to ensure that he does not incur a significant loss on his existing bond portfolio in the short term.

After a thorough discussion with Charlie we mapped out a few trade ideas. We sold a couple of his longer term bonds and reduced his overall fixed income by ten per cent. With the proceeds from selling the fixed income, we allocated some to increasing cash and the remainder to equities. We explained to Charlie that the downside to increasing cash is that it currently earns only 1.25 per cent. After Charlie pays the 30 per cent tax on the interest income his after tax rate of return of 0.875 per cent is less than the rate of inflation. On this portion of Charlie’s portfolio he will not be earning a real rate of return; however, Charlie understands that this is intended to be a shorter term strategy. In managing risk, we felt that a small after tax return would be better than a negative return on his longer term bonds if rates rise. As Charlie requires income from his investments some of the proceeds from selling two of his bonds went to purchase lower risk dividend paying equities. Charlie was pleased that these trades actually increased his after tax rate of return once the dividend tax credit was factored in. The potential for the value to increase through capital gains was also appealing. The downside that needed to be weighed is that equities and the stock market could decline.