# The Great Pension Experiment Part II: Analysing my Options

**Posted:**November 24, 2016

**Filed under:**Strategy |

**Tags:**commuted value, optrust, pensions, the great pension experiment Leave a comment

This is part 2 in a 3 part series I have entitled “The Great Pension Experiment”. This will detail my analysis on what to do with a defined benefit pension plan payout, after leaving my previous employer.

I am a big fan of Monte Carlo analysis (MCA). In a nutshell, when performing an MCA we run a test a fixed number of times, using a controlled set of inputs, and observe the results.

I had mentioned on my previous entry that I felt I could do better than the $600 per month defined benefit pension that OPTrust was offering after I left the company. But, how would I quantify this?

I wanted my LIRA to be as simple as possible, to run virtually effortless. Because of this, I elected to use one of the Couch Potato model portfolios, specifically the one using ETFs. Within these options, given my 25+ year time horizon, I elected to use the *Assertive Portfolio*, which has the following composition:

- 25% of the Vanguard Canadian Aggregate Bond Fund ETF, VAB
- 25% of the Vanguard FTSE Canada All Cap Index ETF, VCN
- 50% of the Vanguard FTSE All-World ex Canada ETF, VXC

The weighted average expense ratio of this portfolio is 0.18% as of November 2016, and the returns are pretty impressive:

- 1-year return: 7.20%
- 3-year return: 12.61%
- 5-year return: 8.91%
- 10-year return: 6.24%
- 20-year return: 7.10%
- Lowest 1-year return (2008-03 to 2009-02): -24.95% (2008 financial crisis)

To perform my analysis, I elected to take the lump sum from OPTrust, and run an MCA on it to see what the projected monthly income would be in 25 years, if I had used the Assertive Portfolio. To do this, I ran 100,000 iterations on 25 years of growth in the portfolio, using randomized returns. Here is an example of one set of returns:

Year | Start Value | % Gain | End Value | Implied Annual Income | Implied Monthly Income |
---|---|---|---|---|---|

1 | $64,723.32 | 14.17% | $73,893.95 | $2,955.76 | $246.31 |

2 | $73,893.95 | 0.01% | $73,900.28 | $2,956.01 | $246.33 |

3 | $73,900.28 | 12.32% | $83,007.73 | $3,320.31 | $276.69 |

4 | $83,007.73 | 10.53% | $91,747.31 | $3,669.89 | $305.82 |

5 | $91,747.31 | 4.52% | $95,898.44 | $3,835.94 | $319.66 |

6 | $95,898.44 | 17.83% | $112,995.45 | $4,519.82 | $376.65 |

7 | $112,995.45 | 16.41% | $131,536.76 | $5,261.47 | $438.46 |

8 | $131,536.76 | 4.38% | $137,296.97 | $5,491.88 | $457.66 |

9 | $137,296.97 | -0.97% | $135,964.84 | $5,438.59 | $453.22 |

10 | $135,964.84 | 20.16% | $163,378.55 | $6,535.14 | $544.60 |

11 | $163,378.55 | 0.01% | $163,400.53 | $6,536.02 | $544.67 |

12 | $163,400.53 | 8.39% | $177,102.35 | $7,084.09 | $590.34 |

13 | $177,102.35 | 9.17% | $193,336.09 | $7,733.44 | $644.45 |

14 | $193,336.09 | 8.17% | $209,128.33 | $8,365.13 | $697.09 |

15 | $209,128.33 | 5.86% | $221,377.33 | $8,855.09 | $737.92 |

16 | $221,377.33 | 9.18% | $241,700.87 | $9,668.03 | $805.67 |

17 | $241,700.87 | -3.10% | $234,207.49 | $9,368.30 | $780.69 |

18 | $234,207.49 | -14.21% | $200,925.08 | $8,037.00 | $669.75 |

19 | $200,925.08 | 8.71% | $218,421.90 | $8,736.88 | $728.07 |

20 | $218,421.90 | -7.81% | $201,370.49 | $8,054.82 | $671.23 |

21 | $201,370.49 | -0.48% | $200,408.22 | $8,016.33 | $668.03 |

22 | $200,408.22 | -3.10% | $194,196.40 | $7,767.86 | $647.32 |

23 | $194,196.40 | -2.32% | $189,688.02 | $7,587.52 | $632.29 |

24 | $189,688.02 | 6.79% | $202,574.08 | $8,102.96 | $675.25 |

25 | $202,574.08 | 10.31% | $223,467.86 | $8,938.71 | $744.89 |

In the above, the % gain is a random gain for the portfolio based on an average return of 8.29%, and a standard deviation of 7.96%. The implied annual income assumes I could take the ending value of the portfolio, and buy an annuity or other similar (set of) instrument(s) to generate *4%* of annual income. I believe 4% annual income, if you are not concerned with growth, is incredibly doable in the market.

But wait, where did that 8.29% average return, and 7.96% standard deviation come from? And what do they mean?

If you take 15 years of returns for the couch potato model portfolio, and do some statistical analysis on that data, you will end up with an average daily return of 0.032%, which equates to an average annual return of 8.287%. Moreover, those same daily returns have a standard deviation of 0.503%, which is 7.959% annualized. (For annualizing, I assume there are 250 active trading days in the year: 52 weeks @ 5 days/week, less 10 days for various holidays). Now, because the model portfolio asks for VAB, VCN, and VXC, and those ETFs are relatively new, I used iShares Core S&P/TSX Capped Composite Index ETF (XIC), iShares Canadian Universe Bond Index ETF (XBB), iShares MSCI World Index ETF (XWD), and iShares Core S&P 500 Index ETF (CAD- Hedged) (XSP) as proxies:

- For the period of October 29, 2009 to December 31, 2015, I used a blend of 25% XIC, 25% XBB, and 50% XWD.
- For the period of April 15, 2002 to October 28, 2009, I used a blend of 25% XIC, 25% XBB, and 50% XSP.

The ETFs listed are iShares ETFs. The XWD is the equivalent to VXC, but prior to October 29, 2009, there were no ETFs I could find that were all-world excluding Canada ETFs. Moreover, the period I chose covers the tail end of the dot-com bubble, as well as the massive 2008 financial crisis. Doing this provides more real world examples. In fact, looking at the above table you can see that in this iteration, in years 18 and 20 the sample has massive declines of -14% and -8% respectively! I feel this is an accurate representation of what *could* happen.

The average and standard deviation play into each iteration of 25 years. In the table above, the “% Gain” column will be, on average, 8.29%, and vary with the standard deviation of 7.96%.

Now, if we pull this all together:

- Create the table above 100,000 times
- Take the final 25 year implied monthly income from each iteration
- Plot a histogram

We get the following:

The above histogram shows that we have a 16% probability of having total monthly income less than or equal to $786. Put another way: we have an 84% probability of having implied monthly income *greater than $786*. If we take this a little further, we have an approximately 7% probability of making at *most $600*, or a 93% probability of making *at least* $600.00. But wait, OPTrust’s defined benefit income would be $600/month. I have only a 7% chance of *not* beating OPTrust’s defined benefit pension! Screw you OPTrust, I’ll take my chances.

So, based on my Monte Carlo analysis, using 13 years of historical returns on a portfolio of 25% Canadian Equities, 50% non-Canadian Equities, and 25% Canadian Fixed Income, I took the plunge to invest all of my money from OPTrust into my LIRA, using the couch potato portfolio. That was almost a year ago. In my next post, I’ll speak to the first year of actual results.

Onward and upward!