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Equity risk in a retirement
portfolio
Paul Snyman & Prof Nico Smith
Introduction and problem statement
• Equity is high risk on the risk spectrum
• Equity content limited due to perception of risk
• Regulation 28 of Pension Funds Act – maximum equity
exposure 75%
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Introduction and problem statement
• Only 6% of retirees are financially independent
(Strydom, 2007)
• Managing volatility vs managing risk?
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Structure of the presentation
• Goal of the study
• Measurement of risk
• Research methodology
• Data analysis and interpretation
• Summary and conclusions
• Managerial implications
6
Goal of the study
The goal of this study was to determine whether volatility
measures, and specifically the standard deviation (STD) of
returns of the FTSE/JSE Top 40 Index (Topi) and the
FTSE/JSE All Share Index (Alsi), would give an appropriate
indication of the risk of including investments in the Topi
and Alsi (equity investments) in a retirement portfolio.
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Review of retirement risk
• Accumulation of the investment phase
• Retirement phase
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Life cycle risk (Malkiel, 2007)
• Appetite for risk
• Risk capacity
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Table 1: Investment composition
based on life cycle position
Source: Malkiel, 2007:346-347
De Villiers-Strijdom study:
• Living annuities with the highest equity content
outperform 80% of other options 80% of the time.
Equities Property Bonds Cash
Mid-20s 65% 10% 20% 5%
Late 30s – early 40s 60% 10% 25% 5%
Mid-50s 50% 12.5% 32.5% 5%
Late 60s 35% 15% 40% 10%
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Variance and
standard deviation (STD)
• Definition
• measure the degree of dispersion from the mean of
the returns of an investment
• Problems
• Normally distributed
• Upside volatility
• Data skewed - measure may become meaningless
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Intrinsic value and volatility
• Definition
• Volatility
• Revert back to intrinsic value
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Research methodology
• Sample
• Indexed Topi and Alsi
• Study period: Topi: 30/06/1995 to 28/02/2014
Alsi: 31/01/1960 to 28/02/2014
• Data collection
• Data analysis
• Target return
• The probability of not achieving the target return
• Monthly returns of the Topi and Alsi
• Volatility of monthly returns of the Topi and Alsi
• Simulation of five sets of actual investments
• Analysis of internal rate of returns (IRRs) of five sets of
simulated investments
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Target return
• Risk in retirement portfolios were investigated during theaccumulation phase and the retirement phase
• Retirement phase risk
• Female retiring at age 65 and living to age 100
• Withdrawal rate 6% (LOA)
• Annual escalation of 6%
• Target return = 11.07%
• If the probability was less than 2.5% for an investment notto obtain the target return, the investment was deemedacceptable for a retirement portfolio.
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95% confidence interval
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2.5% 2.5%
Volatility of the Topi
Average return: 16.80% (annualised)
Standard deviation: 20.40% (annualised)
Kurtosis: 2.50
Skewness: -0.60
Number of data points: 225
Returns < 11.07% p.a. (target return) 103
Table 2: Volatility analysis of the monthly returns of
the Topi
• The expected return at 2.5% downside probability level
is [16.80 - (1.96 x 20.40)] = -23.18%
• The estimated probability of a return less than the target
return of 11.07% is (103÷ 225) x 100 = 45.8%
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Volatility of the Alsi
Average return: 18.24% (annualised)
Standard deviation: 20.96% (annualised)
Kurtosis: 1.49
Skewness: -0.47
Number of data points: 649
Returns < 11.07% p.a. (target return) 284
Table 3: Volatility analysis of the Alsi
• The expected return at 2.5% downside probability level
is -22.84%.
• The estimated probability of a return less than the target
return of 11.07% is 43.8%.
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Simulated investments
• Five sets of simulated investments:
•Set A – investments in the Topi
•Set B – investments in the Alsi with a maximum term of 30
years
•Set C – investments in the Alsi with a maximum term of 20
years
•Set D – living annuities in the Topi
•Set E - living annuities in the Alsi
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Simulated investments – Topi (set A)
Figure 1:IRRs generated by the investments of Set A
• The IRRs of investments are plotted against the
commencement date of an investment. The red lines
indicate that an investment with a commencement date
of 31/12/1996 realised an IRR of 15.8%.
• Target return = 11.07%
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Simulated investments - Topi
Table 4: Volatility of the IRRs of the investments of Set A
Average IRR: 15.94% p.a.
Standard deviation: 0.22%
Kurtosis: -0.30
Skewness: -0.46
Number of data points: 105
IRR< 11.07% p.a. (target return) 0
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Volatility of the Topi
Average return: 16.80% (annualised)
Standard deviation: 20.40% (annualised)
Kurtosis: 2.50
Skewness: -0.60
Number of data points: 225
Returns < 11.07% p.a. (target return) 103
Table 2: Volatility analysis of the monthly returns of
the Topi
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Simulated investments - Topi
Table 4: Volatility of the IRRs of the investments of Set A
Table 5: Probabilities of downside IRR of the investments in
Set A
Average IRR: 15.94% p.a.
Standard deviation: 0.22%
Kurtosis: -0.30
Skewness: -0.46
Number of data points: 105
IRR< 11.07% p.a. (target return) 0
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Simulated investments – Alsi 30 yr.
max. (set B)
Figure 2: IRRs generated by the monthly investments of Set B
Target return = 11.07%
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Simulated investments – Alsi
30 yr. max. (set B)
Table 6: Volatility of the IRRs of the investments of Set B
Average IRR: 16.64% p.a.
Standard deviation: 1.54%
Kurtosis: -1.29
Skewness: 0.57
IRR< 11.07% p.a. (target return) 0
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Volatility of the Alsi
Average return: 18.24% (annualised)
Standard deviation: 20.96% (annualised)
Kurtosis: 1.49
Skewness: -0.47
Number of data points: 649
Returns < 11.07% p.a. (target return) 284
Table 3: Volatility analysis of the Alsi
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Simulated investments – Alsi
30 yr. max. (set B)
Table 6: Volatility of the IRRs of the investments of Set B
Table 7: Probabilities of downside IRR of the investments in
Set B
Target return = 11.07%
Average IRR: 16.64% p.a.
Standard deviation: 1.54%
Kurtosis: -1.29
Skewness: 0.57
IRR< 11.07% p.a. (target return) 0
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Simulated investments – Alsi
20 yr. max. (Set C)
Figure 3: IRRs generated by the monthly investments of Set C
Target return = 11.07%
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Simulated investments – Alsi
20 yr. max. (Set C)
Average IRR: 17.32% p.a.
Standard deviation: 2.73%
Kurtosis: -0.79
Skewness: 0.56
IRR< 11.07% p.a. (target return) 0
Table 8: Volatility of the IRRs of the investments of Set C
Table 9: Probabilities of downside IRR of the investments
in Set C
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Simulated investments – Living
annuities in the Topi (Set D)
Figure 4: IRRs generated by the monthly investments of Set D
Target return = 11.07%
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Simulated investments – Living
annuities in the Topi (Set D)
Average IRR: 14.67% p.a.
Standard deviation: 1.94%
Kurtosis: -0.59
Skewness: 0.41
IRR< 11.07% p.a. (target return) 0
Table 10: Volatility of the IRRs of the investments of Set D
Table 11: Probabilities of downside IRR of the investments
in Set D
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Simulated investments – Living
annuity in the Alsi (Set E)
Figure 5: IRRs generated by the monthly investments of Set E
Target return = 11.07%
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Simulated investments – Living
annuity in the Alsi (Set E)
Average IRR: 15.40% p.a.
Standard deviation: 1.80%
Kurtosis: 0.59
Skewness: -0.31
IRR < 11.07% p.a. (target return) 7
Table 12: Volatility of the IRRs of the investments of Set E
Table 13: Probabilities of downside IRRs of investments in
Set E
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Summary and conclusion
• Risk retirees can tolerate
• Problem – risk to invest in equity is overstated
• Leads to the underutilisation of equity
• Volatility is not risk
• Target return
• Investment risk was measured as the
probability of not realising the target return:
=< 2.5% for the risk to be acceptable for a
retirement portfolio
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Summary and conclusion continue
• Volatility of the Topi
• STD = 20.40%
• Estimated probability of not achieving the target
return = 45.8%
• The volatility of the Alsi
• STD = 20.96%
• Estimated probability of not achieving the target
return = 43.8%
• This risk profile indicated that the Topi and
Alsi did not consistently obtain the target
return of 11.07%.
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Summary and conclusion continue
• Five sets of actual investments in the Topi and Alsi were
simulated (set A to E).
• IRR of each investment was determined.
• Volatility of investments of Sets A to E measured by the
STD ranged between 0.22% and 2.73%.
• Estimated probability of not reaching the target return of
11.07% ranged between zero and 1.3%.
• Risk of each of the five simulated sets of investments
was acceptable for a retirement portfolio.
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Conclusion
• Risk analysis should be based on the IRRs of
long-term investments and not on short-term
fluctuations of returns.
• Volatility measured by the STD of returns does
not provide an accurate measure of risk in
equity investments in a retirement portfolio.
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Managerial Implications
• Redefine risk in retirement portfolios
• Probability that IRR is less than a target return
• Increase utilisation of equity in retirement portfolios
• Don’t forget the upside!
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THANK YOU.
QUESTIONS?
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