Duke of Marmalade
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Thanks for that. As this seems to be work in progress you might like to feedback that the Longevity Adjusted Success rate is not a true reflection of the concept discussed in the Blanchett paper.
Blanchett considers the probability that a withdrawal strategy will fail within a chosen number of years but at a time when one or other of the parties are still alive. This is demonstrated at long durations to be a mere fraction of the probability of failure but paying no attention to whether failure occurred when either of the parties are still alive. Thus you might find that a 4% withdrawal strategy has a 10% chance of failure in 30 years, but it only has a 1% chance of failing in those 30 years whilst one or other of a 65 year old couple are still alive. So the Portfolio Success Rate at 30 years would be 90% and the Longevity Adjusted Success rate would be 99%.
So it is a valid metric to consider. But the App does not calculate the Blanchett LAS correctly - it should never increase with increasing duration. The App appears to use the kitces metric which does increase after a certain duration and indeed when we get to the end of the mortality table and there is no chance of survival the kitces metric becomes 1 no matter what the withdrawal strategy. kitces is saying "you have no chance of surviving that long so why worry, the adjusted success rate is 100%". Not a useful metric.
I earlier gave the formula for Ultimate LAS. The following is the formula for a chosen number, N, of years and is what should be in the graphic.
LAS(N) = sum from 0 to N of d(n) x p(n); plus s(N) x p(N)
where p(i) is the probability of success over i years of the withdrawal strategy unconditional on survival
d(i) is the probability that the party (or the second of joint parties) dies in year i
s(i) is the probability of survival of either party to year i
In words, the LAS over N years is the sum of the probabilities that the party(s) died in the preceding years multiplied by the probability that the withdrawal strategy was successful at least till the date of death, PLUS the probability that the party(s) survived the N years multiplied by the probability that the withdrawal strategy was successful for N years.
This metric decreases slowly until at the end of the mortality table it is equal to the Ultimate LAS for which I gave the earlier formula.
Blanchett considers the probability that a withdrawal strategy will fail within a chosen number of years but at a time when one or other of the parties are still alive. This is demonstrated at long durations to be a mere fraction of the probability of failure but paying no attention to whether failure occurred when either of the parties are still alive. Thus you might find that a 4% withdrawal strategy has a 10% chance of failure in 30 years, but it only has a 1% chance of failing in those 30 years whilst one or other of a 65 year old couple are still alive. So the Portfolio Success Rate at 30 years would be 90% and the Longevity Adjusted Success rate would be 99%.
So it is a valid metric to consider. But the App does not calculate the Blanchett LAS correctly - it should never increase with increasing duration. The App appears to use the kitces metric which does increase after a certain duration and indeed when we get to the end of the mortality table and there is no chance of survival the kitces metric becomes 1 no matter what the withdrawal strategy. kitces is saying "you have no chance of surviving that long so why worry, the adjusted success rate is 100%". Not a useful metric.
I earlier gave the formula for Ultimate LAS. The following is the formula for a chosen number, N, of years and is what should be in the graphic.
LAS(N) = sum from 0 to N of d(n) x p(n); plus s(N) x p(N)
where p(i) is the probability of success over i years of the withdrawal strategy unconditional on survival
d(i) is the probability that the party (or the second of joint parties) dies in year i
s(i) is the probability of survival of either party to year i
In words, the LAS over N years is the sum of the probabilities that the party(s) died in the preceding years multiplied by the probability that the withdrawal strategy was successful at least till the date of death, PLUS the probability that the party(s) survived the N years multiplied by the probability that the withdrawal strategy was successful for N years.
This metric decreases slowly until at the end of the mortality table it is equal to the Ultimate LAS for which I gave the earlier formula.
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