Tuesday, March 25, 2014

Making Decisions when Facing Uncertainty


A way to think about risk

Using an example, I'd like to show how risk theory can help us manage our uncertain future. Risk theory is a branch of mathematics that provides a framework for making decisions with uncertain outcomes.

When it comes to retirement, we are facing the unknown: we don't know how long we'll live and what will be  the rates of investment returns earned on funds used for retirement income. Also, expenses are unknown because of future inflation and the possibility of health-related and other expenses such as long-term care down the road.

Knowing the range of possible outcomes is our starting point to manage uncertainty.

Framework

The starting point of risk theory is the set of possible uncertain environments. Decisions we make influence the results we get in the environment that prevails.
Decisions + Environment = Results
For each decision there is a probability distribution. Making the best decision means choosing the "best" distribution of results among those available.

Example

Suppose I am retiring with a nest egg of $1 Million.

Decision

I am considering two withdrawal options:
  • Spending $50,000 per year  (5% of my initial capital), or
  • Spending $70,000 per year  (7% of my initial capital).
In both cases, my annual withdrawal will increase each year by the rate of inflation, so my purchasing power is preserved.

Environment

My environment is an uncertain future with unknown longevity, rates of investment returns and inflation. I will run out of money if the returns are too low, the inflation too high, or if I live too long.

This may happen whether I decide to spend 5% or 7%, but it is more likely if I decide to spend the higher amount of 7% annually.

Results

Let's define a simple range of possible results that can occur for my retirement:

Awful
I ran out of money and spent several years penniless
Bad
I ran out of money at the end of my life while curbing my spending throughout retirement
Good
I didn't run out of money but had to curb my spending
Excellent
I didn't run out of money and enjoyed a good standard of living

We can calculate odds for each decision that we make. Let's go with the probabilities below for our example. They're in line with these types of calculations and will be sufficient for our purposes.

Probabilities for 5% spending decision

Awful
Bad
Good
Excellent
0%
30%
70%
0%

Probabilities for 7% spending decision

Awful
Bad
Good
Excellent
70%
0%
0%
30%

So for the 5% spending decision, I have a 70% chance of a "good" result and a 30% chance of a "bad" result. With 7%, results are more extreme: the higher spending rate decision will be "excellent" if I live just the right number of years and earn decent returns under moderate inflation. But if things go wrong, I will be poor and destitute and it will be truly "awful".

Utility

My optimal decision means that I must choose the probability distribution that has the best overall outcome for me.

A common approach consists in assigning an "utility" to each result, and calculating the expected utility of each decision. I then choose the  decision that has greatest expected utility.

I will assign a rating from 0 to 10 to the utility of each possible result. The rating is arbitrary but one with which we are familiar.

Value
Utility
Awful
0
Bad
3
Good
6
Excellent
10

And the winner is...

Now we have all the ingredients to calculate the "expected utility" of each decision.

Decision
Calculation
Utility
Spend 5%
0% * 0 + 30% * 3 + 70% * 6 + 0% * 10
5.1
Spend 7%
70% * 0 + 0% * 3 + 0% * 6 + 30% * 10
3.0

Not surprisingly, the 5% middle of the road approach is more sensible. The odds of "excellent" are too low to add a significant utility to this decision.

This is sensitive to the rating and the odds we assign to each result. You can see that I'll need a 50% chance of success with the 7% spending decision to match the utility of the lower spending decision. But even at 50% it is still a big gamble.

What if

What if I have lifetime income, say public pensions and an annuity that are sufficient to cover my essential expenses? Now my nest egg is only for discretionary expenses such as travel, leisure and bequest.

My results will be different: if I run out, it's not so "awful", it's just bad! My life will just have less leisure but I won't be destitute.

7% spending decision

Awful
Bad
Good
Excellent
0%
70%
0%
30%

And here's my new utility with the 7% spending decision:
0% * 0 +70% * 3 + 0% * 6 + 30% * 10 = 5.1
Now both spending decisions are just as good.

Theory and practice

This framework is a way to apply some logic to help us take decisions. It can help with any type of situation.

With retirement, we cannot know how the future will unfold, and in spite of the uncertainty we need to make decisions that involve risk. Results of our decisions are influenced not only by our decisions, but also by the range of outcomes.

By keeping our options open and monitoring our progress, we can take corrective action mid-course to mitigate the damage if our decisions turned out to be not "bad" but "awful".


Tuesday, March 4, 2014

Monte Carlo Details



Question:

How are the economic scenarios used in the Monte Carlo simulations generated? Are they generated within the software, or does the software contain a set of hundreds of scenarios that are used when necessary?

I am trying to understand the stochastic projection component of this software better.

Any more information on this aspect of the software would be appreciated. Thanks.

Answer:

The random scenarios are generated assuming rates of returns of each asset class follow a lognormal distribution. Expected returns and standard deviations are based on historical information adjusted for current trends.

Random numbers are generated using Microsoft's random number generator. Each time the program runs a set of simulations the returns are generated based on the random number generator.

There is a blog post about Monte Carlo simulation:

http://retireware.blogspot.ca/2012/05/monte-carlo-simulation-is-mathematical.html

You will also find some information in the RetireWare help files:

https://secure.retireware.com/web/mc_help.aspx?language=en-CA&node=108&id=res_MChelp2.htm

On a related matter, this is a blog post about risk analysis and our approach:

http://retireware.blogspot.ca/2013/12/quantifying-risk.html

Special Expenses



Question:

I have been using RetireWare to elaborate several files to plan our retirement. I have been trying to include the sale of our actual house in two years, for example, and buy a new one at a higher price in the same year.

I cannot find any place in any of the topics where such a financial exercise is possible. Il could also be the sale of a house and the purchase of a sailboat or a motor home or whatever and its sale several years later.

Maybe another way to look at it would be to add a section where we can simulate an important withdrawal from a particular sources of cash. There is already a section where you can indicate a source of additional assets.

Answer:

Please note that in the Forecast page you can enter special periodic expenses on the Retirement Income Target tab. If it is a one-time expense, enter "0" as the frequency. Frequency of 1 means annual, 2 every two years and so on.

These can be used for one-off items purchased as part of your retirement budget.

Also, in 'Budget Information', you can set up a short-term or medium-term non-retirement savings plan for acquiring a new asset or purchasing some expensive goods such as a boat.

If you want to model the purchase of a more expensive home, keep the current residence and add the difference as an 'Other Property' on Financial Information page. For example, if your house is worth $500,000 and the next house is $600,000, enter $100,000 as 'Other Property' (and the extra mortgage if any).

Pre-retirement Budget


Question:

When doing a pre-retirement budget for a couple I enter the budget under one of the individuals and it still shows a budget for the other spouse. Why?

Answer:

For pre-retirement, each spouse has their own budget relative to income. In your case, you put the budget under one spouse and have not completed a budget for the other spouse.

In cases where there is no budget, the program assumes a default budget equal to after-tax income less savings. So for pre-retirement, it's best to complete a budget for each spouse commensurate with their income, or complete no budget for either spouse.

Dividend Stream



Question:

Is there a way to create another post retirement income stream of dividends from a holding company and are they treated as eligible or non-eligible for tax purposes?

Answer:

There is only one stream of dividends and they are taxed as eligible dividends. Other temporary streams of income can be entered on the 'Other Income' tab on the Finances page.

They are taxed as regular income, so you may have to modify the value to reflect their different tax status if they are non-eligible dividends.

Update Wizard



Question:

One question on the “Update” feature.  I haven’t used it yet but just trying to figure out what happens when you use it. 

So say you update all the financial information and any changes that might need to be done with assumptions, etc.,  does the program then use those numbers and the date (for example if I updated the financial information to February 28th) and project the year-end results for this year based on 10 months of returns / expenses?

If you use the update feature I assume it changes the “date of financial information” to the current month. Correct? If you just go in and make changes to the data then it will be using the previous date for calculations unless you manually change the “date of financial information”. 

Basically the update feature seems to be an automated feature that adjusts the date for calculations and allows you to update the financial information. 

If you need to do more than that then you can go into the other sections to do that.

Answer:

This is correct. The Update Wizard gathers all main and changing data entries in one location (mostly asset values), and updates the date as you describe.

If you use the Detailed or Quick retirement calculations, you must change the date manually.

If you go through the Update Wizard, you can always go in the Detailed Retirement calculation and change the date back if you wish. It is not cast in stone. However, it's best to update the date if you update the market values.

Summary Tables



Question:

Why TFSA’s do not show under the future assets table? They are definitely being saved as per the detailed income statements.

Answer:

Because of space constraints the tables showing on the page (and in the report) can only display a limited number of columns.

Accordingly, we've combined TFSA and registered assets on the table, as TFSAs are a type of registered savings with contribution limits and tax-favoured investment income.

The detailed pop up table shows each account type in much greater detail. It can also be copied and pasted in a spreadsheet or word processor. 

'What If' Scenarios



Question:

My spouse and I are recently retired with DB pension, SERP payouts, CPP and RSP's. I need to know when to draw down RSP's in order to minimize tax and minimize OAS claw-back. Does this function exist in RetireWare?

Answer:

You can try various scenarios for the DB pensions and SERPS to see what works best. If you are well-funded, the RRSP withdrawals would start at the latest age. If you want to withdraw RRSPs at an earlier age, you could enter your estimated annual income from RRSPs in 'Other Income' and see the impact of withdrawing them over a few years to minimize claw-back, instead of dragging it out with minimum withdrawals.

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