Daily Speculations The Web Site of Victor Niederhoffer and Laurel Kenner

12-May-2006
Lifespan Perception, by Kim Zussman

Last weekend we visited friends for their son's 6th birthday. It was an outdoor affair which we attended last year; only it seemed just a few months ago. Most will be familiar with the sensation of the acceleration of time's passage: You graduate, get married, work a while, kids are born, they go to school, and like a cruel joke now they are graduating.

This relates to investing; since gross annual returns come to you faster each year, there is a sensation of wealth building derived merely from acceleration of the passing of time. A common explanation for time-perception acceleration is that when we are young a year is a big fraction of our experience, but as we age this fraction gets smaller. To the extent that this explains the effect, the passage of each year "feels" like 1/age.

The 1/age effect can be related to life expectancy as the sum of fractional experienced years for the remaining years of life. For example, from social security actuarial life-tables, a 51-yr-old male lives on average another 27 years. Each of the subsequent years passes faster than the prior, according to the 1/age assumption. So the perceived lifespan to 78 from 51 is sum (1/age) for all the remaining 27 years.

The method sum(1/age) for remaining years was calculated for life expectancies of a male for each year 1-85. This is plotted here, and shows the marked decline in "how long remaining life feels" as a function of age and life expectancy. An equation that fits the data reasonably well is:

The regression equation is:

exp per = 3.789 - 0.1709 age + 0.002939 age**2 - 0.000017 age**3

S = 0.197146   R-Sq = 95.8%   R-Sq(adj) = 95.6%

Here is the data, the left column age and the right life-expectancy perception ( sum[1/age] for years of expected life for each age:

Age LE perc
1  4.90
2  3.90
3  3.40
4  3.07
5  2.82
6  2.62
7  2.45
8  2.31
9  2.18
10 2.07
11 1.97
12 1.88
13 1.80
14 1.72
15 1.65
16 1.58
17 1.52
18 1.46
19 1.41
20 1.35
21 1.30
22 1.26
23 1.21
24 1.18
25 1.14
26 1.10
27 1.06
28 1.02
29 0.97
30 0.95
31 0.92
32 0.89
33 0.86
34 0.81
35 0.80
36 0.77
37 0.74
38 0.71
39 0.70
40 0.67
41 0.65
42 0.62
43 0.60
44 0.58
45 0.55
46 0.53
47 0.51
48 0.50
49 0.48
50 0.46
51 0.44
52 0.42
53 0.40
54 0.40
55 0.38
56 0.36
57 0.34
58 0.32
59 0.31
60 0.30
61 0.29
62 0.27
63 0.25
64 0.25
65 0.23
66 0.22
67 0.22
68 0.20
69 0.19
70 0.18
71 0.17
72 0.17
73 0.15
74 0.14
75 0.14
76 0.12
77 0.12
78 0.11
79 0.11
80 0.10
81 0.09
82 0.08
83 0.08
84 0.08
85 0.07