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Equity risk in a retirement portfolio Paul Snyman & Prof Nico Smith

Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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Page 1: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

Equity risk in a retirement

portfolio

Paul Snyman & Prof Nico Smith

Page 2: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 3: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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Page 4: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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Page 5: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

Introduction and problem statement

• Only 6% of retirees are financially independent

(Strydom, 2007)

• Managing volatility vs managing risk?

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Page 6: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

Structure of the presentation

• Goal of the study

• Measurement of risk

• Research methodology

• Data analysis and interpretation

• Summary and conclusions

• Managerial implications

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Page 7: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 8: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

Review of retirement risk

• Accumulation of the investment phase

• Retirement phase

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Page 9: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

Life cycle risk (Malkiel, 2007)

• Appetite for risk

• Risk capacity

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Page 10: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 11: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 12: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

Intrinsic value and volatility

• Definition

• Volatility

• Revert back to intrinsic value

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Page 13: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 14: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 15: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

95% confidence interval

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2.5% 2.5%

Page 16: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 17: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 18: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 19: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 20: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 21: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 22: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 23: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 24: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 25: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 26: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 27: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 28: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 29: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 30: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 31: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 32: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 33: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 34: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 35: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 36: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 37: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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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Page 38: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

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Page 39: Equity risk in a retirement portfolio - FPI. Equity_risk_in...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%

THANK YOU.

QUESTIONS?

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