How can you calculate bond duration?

Bond duration measures a bond's sensitivity to interest rate changes, indicating its price volatility. To calculate: Multiply each cash flow by the time until receipt, then divide the sum of these products by the bond's current price. Divide Macaulay Duration by 1 plus the periodic yield-to-maturity rate (expressed as a decimal) divided by the number of payment periods per year. Measures a bond's sensitivity to changes in yield, considering potential changes in the bond's cash flows due to embedded options or features. It's calculated as the percentage change in price for a 1% change in yield. Using these methods, investors assess how bond prices might change with fluctuations in interest rates, aiding in investment decisions.

Duration can be interpreted and can be useful solely in comparison to the durations of other bonds or financial instruments. Such comparisons are regularly made in various scenarios. For instance, a bond portfolio manager, under specific economic conditions, decides to increase or decrease holdings in bonds with longer durations. In macroeconomic analysis, consider the instance when a yield curve characteristic to the current economy is formed. The yield curve is constructed using bond durations. Another financial example arises when a company prepares for a bond issuance. Comparing the duration of the intended bond to the yield curve provides a benchmark for anticipating the yield during the issuance.

Given it is a simple number taken in isolation, taking duration and not considering its construction and form is a signficant oversimplification. Reflect on how a 30 year bond and a zero coupon bond could have the same durations but very different appearances beyond their identifical durations.

Duration risk in a default-free bond portfolio relies on the assumption that the only source of risk is a parallel shift of the yield curve. The caveat though is you assume the yield curve has one shape, and information is lost by summarising the risk characteristics into one number. The curve shape is dynamic – the slope can flatten, steepen, as well as twist. The assumption of one source of risk quickly becomes unusable. However, key-rate duration accounts for non-linear changes in shape and considers changes along the yield curve at specified points. This makes for better risk management when constructing a hedging strategy or replicating risk profiles. More importantly, you are not making a simplifying assumption of one source of risk.

With Modified Duration, it’s providing a linear estimate and, in terms of absolute value, the change is the same whether it’s an increase or decrease in yield-to-maturity. But the thing is, for a given coupon rate and time-to-maturity, % price change is greater in absolute value when rate goes down vs when it goes up. So you need to do Convexity Adjustment, as this accounts for the convex curve relationship between bond price and yield-to-maturity. Without getting too technical, an example could show that, for a bond, if the yield jumped by 100bps or fell by 100bps then you would have: Jumps 100bps: loss in value of bond = X% Drops 100bps: gain in value of bond = gain in value of bond >X%

One of the enduring challenges of duration is the trajectory of the yield curve and relationship between short and long term rates. This can give a misleading comparison between bonds at different coupon rates and different maturities on and off run. Not a major consideration in an extended disinflationary period since 2012 but has very much been the case since 2022. In some ways we can step back if we take a hold to maturity perspective. Some may suggest using convexity to adjust the price change estimate and that helps but I would suggest far more practical measures are DTS *since we can consider ‘spread’ a dirty indicator of rate surprises and market volatility, plus estimating the duration of a bond for different maturities and Refi.

How to buy bonds and create a portfolio? Its not simple and straightforward, esp if the awareness and understanding is low. This is a specialized subject and needs technical expertise. Hence I trust Debt Mutual Funds. But even there...i have a slightly diversified investment strategy- across short and long duration bonds.