In our last article, we described the benefits of diversifying between stocks and bonds and how adding some long-dated Treasuries to a stock portfolio can be very additive in terms of risk-adjusted returns. In that article, we mentioned that a bond ETF's long-term returns are highly dependent on their current yield and now we want to expand upon that idea in greater detail. This relationship between yield and returns might seem obvious since it holds for individual bonds, but most fixed income ETFs keep a constant maturity by selling bonds that are rolling out of their maturity window (e.g. 20+ years for the iShares 20+ Year Treasury Bond ETF (NYSEARCA:TLT), 7-10 years for the iShares 7-10 Year Treasury Bond ETF (NYSEARCA:IEF) and 10+ years for the Vanguard Long-Term Corporate Bond ETF (NASDAQ:VCLT) - these are three ETFs in the WCM model portfolios) and therefore an investor could take losses year after year, as interest rates rise and the bonds that roll out of the maturity window are continuously sold at a loss. What are the expected returns for such a situation? With the buying and selling of the bonds in the portfolio, it becomes more complicated, but we're going to try to answer this question.

Before getting into expected returns, we want to spend a little time investigating what causes interest rate moves. Bonds are contracts that provide specific payments over a fixed time period. You know how much and when you're going to get paid when you buy a bond. We want to focus on Treasuries here and ignore the potential for default to keep this simple. The basic concepts apply to investment-grade corporate bonds as well, with the credit spread over Treasuries mainly due to the risk of corporate default. Going back to Treasuries, an investor knows the future payments so the main thing she is worried about is the purchasing power of those future dollars. Simply put, inflation is the real concern. If a Treasury bond's current yield is lower than the rate of inflation, then those future dollars will have less purchasing power than they do today and investors will choose to sell the bond today (pushing up its yield) and spend the money or buy something else that will outpace inflation. Since we don't know what future inflation will be, investors expect some added premium for holding a bond that has an uncertain future value. In the chart below, we see that interest rates are generally higher than recent levels of inflation measured using the annual change in the Consumer Price Index or CPI. This differential can be attributed to the risk premium that investors demand to hold Treasury bonds that can fluctuate in value (price risk) between today and when they mature.

From this chart, we can see that as we described above, interest rates are driven by inflation. There are a lot of other factors, but in large part, inflation is the key to interest rates. Another factor that comes into play, especially today, is the level of short-term interest rates, which are largely controlled by the Board of Governors of the Federal Reserve, more commonly known as the Fed. In the chart above, the 10-year Treasury interest rates stayed higher than the rate of inflation in the early 1980s because the Fed was keeping short-term interest rates high even after inflation started to come down. This kept the long-term interest rates high as well. Who is going to buy a 10-year bond that yields 5% to 6% (arguably a fair value when inflation is running at 3% to 4% like it was between 1983 and 1985) when the 3-month Treasury bill yields 8% to 10% (as was the case between 1983 and 1985)? Thus, the Fed kept short-term rates high in the early 80s and affected long-term rates in the process. Now, they are keeping short-term rates low and are dampening long-term rates as they have set out to do. Whether this is going to do what they want to the economy (raise employment and economic growth) is debatable and not something to cover in this article. The current Federal Reserve is primarily focused on their dual mandate of full employment and reasonably low inflation (current target is 2%). Since there are no clear signs of inflation rising today and we at Wynn Capital don't expect that to change until the labor market improves enough to generate wage inflation, we expect they keep short-term rates low longer than most expect. This is likely to keep long-term rates low for longer as well. Even if they do raise rates in the next year, that will likely reduce inflation expectations enough to dampen any rise on long-term interest rates.

We know that there are plenty of other factors that can move long-term interest rates besides inflation and Fed policy, but those two go a long way and most other factors are minor in comparison. Rather than delve any deeper on that topic, let's move on to expected returns for a constant maturity bond portfolio. ETFs just haven't been around long enough to put together a robust long-term historical analysis of yield versus subsequent returns, so another method is needed. For those not interested in the mathematical model for how we estimate bond returns, just skip to the next chart for the results of our analysis of bond yields and subsequent returns.

The St. Louis Federal Reserve has an excellent database of economic and market data (commonly referred to as the FRED database) going back many decades, so I have chosen to use yield data from that source. In order to calculate returns, we need a pricing model for bonds. It's fairly straightforward to build an accurate model for the total return of a fixed-coupon bond over the first month after issue with the two inputs of yield and maturity. For those interested in a bit more detail, we use a first order model that only considers the carry or interest accrued and the price change calculated by duration multiplied by change in yield.

The above equation only describes the price change due to changes in interest rates, not the interest accrued. When interest rate changes are small, as is almost always the case over a 1-month time horizon, these two factors very accurately model the total return of a bond. Since the FRED database has data on newly issued bonds we know the coupon is generally equivalent to the interest rate which simplifies the calculation of the bond's duration. This leaves the problem of needing to roll to a newly issued bond each month since we are using the interest rate data for newly issued Treasuries, but we can make a reasonable assumption that the returns for bonds whose maturity is close to (within 6-12 months) that of the newly issued bond are the same as that of the newly issued bond. Then the holding period can be extended and we have a model for the returns of a plausible bond portfolio. In the chart below, we show the results for our model using the FRED data on the constant maturity 10-year US Treasury rate.

We have chosen to use the 10-year US Treasury in our example because it has maximum time to maturity that also has a enough historical data to go back to a period of rising interest rates. The 30-year US Treasury was first issued in 1977, so it was only around for 4 years of the rising rates period that started in the 1950s. Some quick statistics between the yield and subsequent returns for the bond portfolio we have modeled using 10-year US Treasury yield data are in the table below. The averages between yields and subsequent returns are very close and the distributions, as measured by the standard deviation, are similar in width. The difference between the two measures (return - yield) has a significantly lower variability due to the high correlation (94%) between yield and annualized return over the next 10 years. Dividing this difference by the yield, we see this variability in the return has a standard deviation of 21% of the initial yield.

If the future looks like the past, then we can apply these statistics to today's level of 2.6% for the 10-year US Treasury. We can expect that a constant 10-year maturity Treasury bond portfolio (for which IEF is an excellent ETF proxy) will return between 2.05% and 3.15% (±21.3% * 2.6% = ±0.55%). If you believe interest rates will rise, then you can take the lower end of that range rather than the middle, but there's not a lot of uncertainty. We are not trying to predict what interest rates will do, but rather give some context to how bonds have performed in the past, in both rising and falling interest rate environments. It gives us some comfort that we know what we will get from fixed income ETFs with almost as much certainty as if we held an individual bond to maturity. Besides the greatly improved liquidity that ETFs provide versus holding individual bonds, another reason to use ETFs like TLT, IEF and VCLT is that they keep their risk profile constant due to the fixed maturity window of the bonds they hold. This is very helpful when building an efficient portfolio that will fit an investor's financial needs and goals.

One final thing to keep in mind. This basic analysis applies for any fixed income fund embedded with a constant maturity window, but the holding period to obtain the high correlation between current yield and future realized returns scales with the fund's maturity (really duration would be an even better measure for those fixed income savvy readers). From further analysis we have done, we see a correlation above 90% and low variation in the difference between yield and future returns when the holding period is at least half of the average maturity. For a fund like TLT, the horizon needs to be 10 years or more. For IEF, 5 years is likely sufficient. This gives us a good sense of what to expect from our fixed income exposures and leaves us with the need for a similar understanding for other asset classes. It gets a lot harder if you don't know when or how much you will be paid in the future, but a similar analysis can be done for equities. The range of outcomes is just wider. Look for my next article to cover that topic.

**Disclosure:** The author is long TLT, VCLT.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.