Interpreting the Macauley and modified duration of a debt instrument

The common measure of loan duration is the Macauley loan duration. Investors and lenders (the two parties who play in the secondary bond/debt market) use the Macauley duration (MacD) to price a loan for arbitrage. Let's calculate a loan duration, compare it to its contractual maturity, and how the duration informs us of the loan's susceptibility to prevailing interest rates.

Note: This is part 2 of loan duration v maturity. You may want to read part 1 before proceeding.

Our healthcare entrepreneur is requesting a $100K loan to fund the purchase of a $200K asset (a financial leverage of 0.5 - a typical amount requested). The APR is 10%, which is divided by 12 to calculate a monthly interest payment of 0.83% (review the different types of interest rates here). The maturity of the loan (maturity ≠ duration) is contractually set at 24 months. 

Total cost of the loan and why the lender won't wait

With the loan parameters above, the entrepreneur will end up paying $110,742.87 at the end of the maturity. The lender will earn an accounting profit of $10,742.87, a respectable return. So why isn't the lender happy with this aggregated payout? Some lenders aren't able to wait 24 months (or more) for such a payout. Banks and other institutional lenders are obligated by law to maintain a certain amount of capital at all times. In short, banks need *dry powder* in order to make more loans and remain compliant with regulations. As a result, it won't come as a surprise to you that as quickly as the ink on your loan documents dry, the lender is already arbitraging your loan on the secondary debt/bond market.

Factors that affect the price of the bond on the secondary market: rating and interest-rate susceptibility

What makes an investor want to buy the debt? First, the investor reviews the bond rating. Bonds are divided into *investment grade* and *speculative grade* (a.k.a. junk bond). The former is desirable but more costly and with a modest return. The latter are less desirable but, if you don't default in the 24-month period, the returns are significantly greater. The bond rating will partially depend on the underlying borrower's (i.e., our entrepreneur's) credit worthiness and default risk (see loan-to-value to learn more about debt underwriting). The bond rating will ultimately be reflected in the price of the bond.

The next parameter affecting the ultimate bond price is its susceptibility to interest rate changes. Remember that the monthly cash inflow of $4,614.49 is contractually fixed. Depending on the prevailing interest rates, the investor may have other options in which s/he can earn a greater monthly cash inflow than this amount. If interest rates rise after the investor purchases the bond from the lender, the new price of the bond will be lower than what s/he initially paid for it. If interest rates fall, the bond's price will increase. The bond's price can't break free from its susceptibility to interest rates, but it can mitigate that susceptibility. Susceptibility to interest rates is quantified by the bond's duration.

The MacD represents the time in which the bond is most susceptible to interest rates, and is a function of the loan interest rate (in our case, 10%) and the maturity (in our case, 24 months). The higher the loan interest rate and/or the shorter the maturity, the smaller the MacD and the less susceptibility the bond has to interest rates.

In our example, for every 1% increase in prevailing interest rates, the bond's price falls by approximately 12%. Smaller ModD values means less volatility in the bond's price - less risk and, concurrently, smaller reward. Remember that for every 1% decrease in prevailing interest rates the bond's price increases by 12%.

In summary, a lender isn't looking at the contractual terms of the loan only. Lenders know that at some point in the future, they'll need to arbitrage the loan - and that arbitrage will depend on the bond's rating (which has a lot to do with the entrepreneur who took on the debt) and the bond's duration (which has a lot to do with the negotiated interest rate and maturity of the bond). Understanding what (de)motivates the lender in a transaction may help you better negotiate debt financing when you're ready to make your next asset purchase.