###### CERF Blog

Interest rates are historically low and so is the return on savings. People commonly talk about low interest rates being an inducement to increase spending and reduce saving. In fact, this is one of the “transmission mechanisms” by which expansionary monetary policy is presumed to stimulate the economy. In economic theory, consumption spending is modeled as an increasing function of wealth, and wealth is a decreasing function of interest rates. The combination implies that savings is an increasing function of interest rates. That is, as interest rates fall asset price prices (think of bond prices, stock prices, housing values, etc.) tend to increase and personal wealth goes up. As people get richer, they are comfortable spending more money.

However, there is another way to look at this. As interest rates fall, while the value of your wealth may increase, the prospective future return on that wealth goes down. If your goal is to achieve a smooth pattern of (real or inflation-adjusted) consumption over time, it may well turn that lower interest rates require a lower level of real consumption. Falling rates may induce less spending and more saving!

In prior essays, I have proposed a very simple rule of thumb regarding sustainable spending. That rule is that you can comfortably spend each year a fraction δ of your total wealth (C=δ*TW where C is consumption and TW is total wealth) where your total wealth includes financial wealth (financial capital) and the present value of your future income (human capital). The proportionality constant δ is the after-tax real rate of return that you earn on your wealth. The logic is simple: if inflation-adjusted wealth increments each year by δ*TW then you can spend that amount without reducing the real value of wealth. Naturally, this means wealth will never decline so it is directly relevant either for people who think they may live forever, or for those who intend to leave a bequest amount equal to current wealth. When interest rates fall, δ declines and TW rises, so without looking at specific numbers, the effect on consumption is not clear. But, with interest rates quite low today it is likely that a further decline in δ would not be offset by a greater percentage increase in wealth. Let’s take a simple example. Suppose δ declines from 3% to 2%; this will entail a reduction in C unless total wealth increases by more than 50%.

Of course, this model is very simple. What if people recognize their mortality and are comfortable in not leaving a bequest? The essential logic still holds. Suppose a fellow is 65 years old, with $1 million net worth, and the average-tax real rate of return is 3%. If we assume the guy knows he will die at age 100, and is willing (maybe eager) to die broke, then we can easily calculate his maximum steady real spending (in Excel, we could use the PMT function) which is $46,539 (=PMT(.03, 40, -1000000)). If the rate of return were to decline to 2%, the same calculation would yield $40,002, a reduction of 14%. This example assumes wealth does not change as the rate of return declines. If the fellow’s wealth increased by more than 16%, then the calculation would produce an increase in sustainable spending.

Next, let’s get rid of the assumption of known mortality. In the (real world) case of uncertain mortality, the investment vehicle that achieves the maximum smoothed consumption consistent with no bequest and zero probability of failure is probably inflation-indexed life annuities (ILA contracts). These are insurance contracts that make a steady real payment every year from the origination date to mortality. They operate very much like Social Security and represent a great tool for handling so-called longevity risk (the risk of living too long). The pricing of ILA contracts is a bit more complex than the fixed annuity discussed above, but the basic idea is to adjust the cash flows by the actuarial probabilities of survival. The bottom line is that the “price” of one dollar of spending in the future is going to be greater as the rate of interest is lower.

In economic theory the key drivers of an individual’s optimal consumption and investment strategies are the individual’s degrees of “time preference” and risk aversion. Time preference is the idea that people prefer consumption today to consumption in the future. For people who are highly impatient, time preference is very high. Such individuals will strongly prefer to spend today, even if this means consumption in the future will be lower. On the other hand, people who very low time preference may well prefer a consumption stream that is rising over time.

My simple model C= δ*TW can accommodate both high and low time preference. If you set your proportionality constant δ greater than the expected rate of return then your consumption (and wealth) will tend to decline over time. Eventually you will have to reduce spending in order to not run out of money. Conversely, if you set δ conservatively, below the expected rate of return, then consumption and wealth will likely increase over time.

When contemplating feasible retirement spending plans, an interesting base case is the maximum level of steady real consumption that is achievable with zero or minimal risk. In principle, I suspect that the portfolio that would generate the maximum smoothed consumption is some combination of Treasury Inflation Protected securities (TIPs) and deferred life annuities. The reason for buying deferred instead of immediate life annuities is that by doing so you achieve greater “mortality credits” (mortality credits represent the portion of annuity yield that is due to the anticipated death rate of a pool of retirees). This problem has a long history. In the next essay, we’ll harken back to a two hundred year old debate on retirement spending between the optimist the Marquis de Condorcet and the pessimist Thomas Malthus.