Glidepath Intuition: Why the equity weight should fall with age

Most financial experts advise investors to follow a glidepath over the retirement savings accumulation phase, i.e., start with an aggressive equity share when young and shift out of equities and into bonds when approaching retirement.

One explanation for a shrinking equity weight is increasing risk-aversion while getting older. While that would definitely create a glidepath, one can show that even a constant risk appetite over the life cycle necessitates a glidepath. If we account for the net present value of a saver’s future contribution and factor this implicit bond allocation into the current net worth and portfolio, we can generate a downward-sloping equity share over the accumulation phase, even with a constant risk tolerance.

To illustrate this intuition, consider an investor, Jim, who starts investing at age 25, makes regular monthly contributions into his retirement plan and likes to retire at age 65. Moreover, Jim has no financial assets at age 25, however, he does have a substantial implicit net worth if he looks at his entire stream of future contributions discounted back into current dollars.

The discounted future contributions at any given time are plotted as the blue in Chart 1. Notice that over time, this future sum of discounted contributions falls and eventually reaches zero upon retirement. 

Chart 1: Projected Time Series of of Jim’s Net Worth Components

For the purpose of this example we assume that throughout his life, Jim has a constant risk preference that makes him prefer a 55% equity and 45% bond portfolio in his lifetime net worth portfolio. If Jim considers the future stream of contributions as a bond-like asset, his initial asset allocation is exactly 100% bonds and 0% stocks, much higher than the targeted bond allocation plotted as the black dashed line. Of course, strictly speaking, the future contributions would be closer to a sequence of inflation-protected zero-coupon bonds, so not exactly a 100% substitute for the bonds we consider in target date glidepaths. Because of this abstraction we caution that the glidepath we construct here is only for illustration purposes to convey the intuition for why the equity glidepath should be decreasing in age. I will perform a more careful glidepath optimization exercise in a future post.

Chart 2: Equity vs. Bond allocation of Jim’s Projected Total Net Worth

Absent a way to short-sell bonds inside the retirement portfolio or borrow against his future contributions, Jim cannot get to his desired total net worth equity portion of 55% for at least a number of years. The best he can do is to invest 100% of new contributions into equities and wait for two developments to unfold:

1. The drop of future discounted contributions denoted by the shrinking blue area over time and, two, 

2. The increase in his total net worth due to capital appreciation, which drags up the target bond allocation, displayed as black dashed line.

At around age 38, the black dashed line indeed goes above the dark blue area and, thus, the remaining implicit bond wealth is now lower than the target. Now it is time to invest in bonds within the financial portfolio, represented by the light blue area. As Jim gets closer to retirement more of the implicit bond wealth is replaced by explicit bond investments and, eventually, Jim reaches retirement at age 65, when he has a 55% stock and 45% bond portfolio and no more future discounted contributions. 

If we now compute the equity share in Jim’s financial portfolio only, we see that the equity portion stays at 100% until about age 38, then declines to the target level of 45% over the remaining work years, see the blue line in Chart 3. Intriguingly, the equity share during the early years, despite standing at 100% within the financial portfolio, is actually lower than the target of 55% when calculating the equity share within the entire lifetime net worth, see the red line in the Chart 3, due to the constraint of not being able to short bonds in the 401(k) plan. As a side note, notice that glidepaths in use in actual target date funds normally start at 90% stocks and 10% fixed income rather than 100% equities, due to ERISA constraints.

Chart 3: Time Series of Equity Shares Jim’s Portfolio

Starting at around 38, while the glidepath (blue line) is decreasing, the equity share inside the total lifetime net worth portfolio (red line) stays constant at the target 55% level. The glidepath slopes down purely due to phasing out the implicit bond wealth from future contributions and replacing them with actual bond investments.

To conclude, I showed that the contribution pattern and the inability to borrow against the net present value of future contributions create a downward slope in the equity glidepath, even with constant risk aversion throughout. The glidepath overcomes impossibility of dis-investing from the bond-like portion of the saver’s net worth.

Of course, the exact shape of the glidepath, i.e., when to start transitioning out of equities and how fast and to what final asset allocation, is a quantitative exercise that requires more careful analysis. We will present the mathematically precise optimization in a future post.