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Nebraska Wealth
Management
Conference 2016
Investment Math
David E. Hultstrom, MBA, CFP, CFA
Investment Math
• Dollar Cost Averaging
• Distribution of Stock Returns
• Covered Call Writing
• Leveraged ETFs
• Pension vs. Lump Sum
David E. Hultstrom, MBA, CFP, CFA
Dollar Cost Averaging
• What most people are actually doing
• On average it’s just half the exposure
• Psychologically it works
• No one really believes it adds actual value
David E. Hultstrom, MBA, CFP, CFA
David E. Hultstrom, MBA, CFP, CFA
Rolling 12-Month Returns in U.S. Stocks (1926-2015)
Normal Curve Historical Data
Distribution of Stock Returns
Out of the 1,069 rolling 12-month periods from
1926 through 2015, if U.S. stock returns were
normally distributed, a return greater than 3σ
(75.6%) should have occurred once. We have had
it happen four times:
• 123.33% in the TTM through May 1933
• 154.60% in the TTM through June 1933
• 100.79% in the TTM through February 1934
• 95.05% in the TTM through March 1934
David E. Hultstrom, MBA, CFP, CFA
Distribution of Stock Returns(Continued)
Out of the 1,069 rolling 12-month periods from
1926 through 2015, if U.S. stock returns were
normally distributed, a return less than 3σ
(-51.50%) should have occurred once. We have
had it happen four times:
• -52.47% in the TTM through March 1932
• -56.84% in the TTM through April 1932
• -60.35% in the TTM through May 1932
• -65.42% in the TTM through June 1932
David E. Hultstrom, MBA, CFP, CFA
Distribution of Stock Returns(Continued)
• Points of (possible) interest:
– Daily vs. Monthly vs. Annually
– October 19, 1087 was a 26σ event (~1/∞)
– You can’t multiply monthly σ by 12 because
momentum
David E. Hultstrom, MBA, CFP, CFA
Covered Call Writing
An Introduction to Synthetic Securities:
S = C - P + T
S - C = T - P
S - C + P = T
David E. Hultstrom, MBA, CFP, CFA
Leveraged ETFs
David E. Hultstrom, MBA, CFP, CFA
1x 2x 3x -1x -2x -3x
Period 1: 25% 50% 75% -25% -50% -75%
Period 2: -20% -40% -60% 20% 40% 60%
Arithmetic Mean: 2.50% 5.00% 7.50% -2.50% -5.00% -7.50%
Geometric Mean: 0.00% -5.13% -16.33% -5.13% -16.33% -36.75%
Pension vs. Lump Sum
• An actual case:
Female, age 56, choice of $1,357,684 lump
or $98,796 life annuity. Pension is almost
fully funded and from quasi-gov’t entity. She
has no dependents or legacy desires.
• $98,796 /$1,357,684 = 7.3% yield?
• IRR to a particular age (better)
• Mortality-weighted IRR (best)
David E. Hultstrom, MBA, CFP, CFA
Pension vs. Lump Sum(Continued)
David E. Hultstrom, MBA, CFP, CFA
