What the plan can afford and the client can stand
Two different questions hide inside 'how much risk?': how big a loss the plan can absorb before essential spending is at risk, and how big a loss the client can watch. The tighter one sets the limit.
- Compute a stress loss and test it against the client's tolerance
- Price the floor of essential spending and derive risk capacity
- Turn each limit into a maximum equity weight and take the smaller
- Say what to tell a client whose tolerance and capacity disagree
The intuition
A wealthy, nervous client has plenty of capacity and little tolerance: the plan could absorb a big loss, but the client would sell at the bottom. A bold client with a thin cushion has the reverse: they would sit through a crash, but the crash would leave essential spending uncovered. Both are real limits. Exceeding tolerance leads to bad behavior; exceeding capacity leads to a plan that fails.
Capacity has a price. The essential spending the portfolio must fund, valued as an annuity at a safe real rate, is the floor; capacity is how far the portfolio can fall before it touches that floor. A stress test then converts each limit into an equity weight: if equities can fall 50% with bonds flat, a 20% tolerance allows 40% equities, and the tighter of the two answers is the recommendation.
Floor = essential spending × (1 − (1 + r)^−N) ÷ r. Capacity = 1 − floor ÷ portfolio. Stress loss = equity weight × equity crash, bonds flat. Maximum equity by capacity = capacity ÷ crash; by tolerance = tolerance ÷ crash. Recommended maximum = the smaller.
Why it works
- The conventions here: a retiree's essential spending, real and paid at year end for N years, is funded from the portfolio at a safe real return. The floor is its present value. Tolerance is the largest one-year loss the client says they can live with. The stress drops equities by a stated amount with bonds flat.
- Price the floor at a safe rate, not the portfolio's expected return. The floor is money that must be there whatever happens; discounting it at a risky return assumes the very risk the floor is meant to rule out.
- Capacity is a share of the portfolio, the part above the floor. A pension or other income that covers some of the essential spending shrinks the floor and raises capacity without any change to the portfolio.
- The stress converts limits into weights. Only the equity sleeve falls, so a limit on the loss divided by the crash is a limit on the equity weight, capped at 100%.
- Whichever binds is the conversation. Capacity binding: the plan cannot afford the risk the client would accept, so less equity or a larger reserve outside the portfolio. Tolerance binding: the plan could afford more, but a portfolio the client abandons in a crash does more damage than one with a lower expected return.
- Questionnaires measure tolerance only. An 'aggressive' score with a thin cushion is still a conservative allocation.
| Annuity factor: (1 − 1.02⁻²⁵) ÷ 2% | 19.523 |
| Floor: $60,000 × 19.523 | $1,171,407 |
| Capacity: 1 − 1,171,407 ÷ 2,000,000 | 41.4% |
| Maximum equity by capacity: 41.4% ÷ 50% | 82.9% |
| Maximum equity by tolerance: 20% ÷ 50% | 40%, so tolerance binds |
| Stress loss today: 60% × 50% | 30%, $600,000: breaches the tolerance |
A pension covering $10,000 of the spending would cut the floor to $976,173 and lift capacity to 51.2%. It would not move the tolerance limit at all.
The formulas
The present value of what must be paid, at a safe rate.
How far the portfolio can fall and still cover the floor.
Bonds flat; only the equity sleeve falls.
Each limit, converted to a weight and capped at 100%.
The tighter constraint wins.
Worked example
Price the essential spending as an annuity to get the floor, then capacity is what is left above it. The follow-up says why the floor is priced at a safe rate.
See it move
Same retiree and the same floor. Change the loss the client says they can live with, how far equities fall in the stress, and the equity weight held today.
- Raise the loss the client can live with. The tolerance bar and its equity weight rise; the recommended maximum rises until capacity takes over, then stops.
- Raise the equity fall in the stress. Both equity limits fall or stay at their cap, and today's stress loss rises.
- Raise today's equity weight. The stress loss rises; neither limit moves, because they describe the client and the plan, not the current mix.
Run it backwards
Capacity and tolerance are known, and so is the stress. What is the highest equity weight that respects both?
Each limit divided by the crash is an equity weight, capped at 100%. Take the smaller; the limit that gave it binds.
The follow-up is what to say to the client, which differs depending on which limit bound.
Traps
Say it in the interview
“This client scores as aggressive but has a thin cushion. How much equity?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Floor = essential spending × annuity factor at a safe rate; capacity = 1 − floor ÷ portfolio.
- Stress loss = equity weight × crash, bonds flat.
- Max equity = limit ÷ crash, for each limit; take the smaller.
- Tolerance is behavior; capacity is arithmetic. Both are real.