# Understanding Monte Carlo

Would anyone here be willing to help me understand the Monte Carlo reports? I start with the following text from the tutorial:

In the process of calculating the entire time path or trajectory of consumption associated with each of the 500 time paths of randomly drawn returns, we also determine the associated time paths of retirement and regular asset levels, income levels, saving levels, etc. After all 500 trajectories of all variables are determined, we do two things. First, we show the percentile distribution of outcomes for the household’s living standard, income, and asset levels in each future year. Second, we rank the 500 trajectories based on the present value of consumption and display the trajectories for the household’s living standard, income, and asset positions associated with the fifth lowest, 25th lowest, 50th lowest, 75th lowest, and 95th lowest present values of consumption. We refer to these as lowest, low, middle, high, and highest trajectories.

So then:

1. What, for example, is meant by "5th lowest present values of consumption"? I don't know what that means. So 95th lowest is associated with "highest trajectory"? Hmm. I don't get that.

I'll stop here and see if anyone replies.

Dan

1

Hi Dan, We are trying to rank the 500 trajectories (outcome paths) we run based on total lifetime consumption. We could just add up, for each trajectory, the annual amounts of consumption and classify the trajectories based on the total. But this would treat \$50,000 of consumption this year and \$50,000 of consumption in, say, 30 years the same. But \$50,000 spent 30 years is not as valuable as \$50,000 today because you can put aside less than \$50,000 today, invest it in safe bonds, and end up with \$50,000 30 years from now. The amount you need to put away today to end upwith \$50,000 30 years from now is called the present value of \$50,000. If, for example, the safe bond rate is 5 percent, the present value of the \$50,000 spent or received 30 years from now is \$11,569. I.e., you can invest \$11,569 this year in 30-year bonds yielding 5 percent and end up with \$50,000 in 30 years. (The formula is that 11,569 times 1.05 raised to the power 30 equals 50,000.)

In determining the present value of lifetime consumption for each trajectory (which we use to rank the trajectories), we first determine the present value of each future year's consumption and then add up these present values. So, in the example above, we are adding the \$50,000 spent this year and the \$11,569 (the present value of consumption spending 30 years from now) together in addition to adding the present values of consumption for all other future years.

Hope this is clearer. If not, call me at 617 834-2148.

best, Larry

What, for example, is meant by "5th lowest present values of consumption"? I don't know what that means. So 95th lowest is associated with "highest trajectory"? Hmm. I don't get that.

2

OK. That helps. Now I understand the concept of "present value" which helps, but just to clarify a bit more:

Your reply indicates that you are accounting for the present value of the consumption figure in each future year. And you explain present value by saying that a consumption number in any future year has a certain present value. Perhaps the example of the present value of 50k because you could invest it and it would grow over 30 years misleads me because I keep thinking: but we are not investing this consumption money. The consumption value in each year is, in the economy of the ESplanner, a post-investment figure. Of course you could invest it or save it, but in fact, it is mostly "consumed," not invested. So how does a consumption value 30 years from now have present value?

Let me try to guess the answer (but I'm not sure of this so help me out): The consumption value 30 years from now reflects or entails the investments such as 403b, ROTH, asset growth, etc. over all the prior years. In other words, in order to have and spend (not invest) that 50k thirty-years from now, I have to invest today. And that's why it's proper to speak of the present value of a future 50k consumption figure. The consumption value of a future year is the outcome of present investment of assets, 403b, etc. (but--and this is my main point/question--not the present investment of my current year's consumption value which got consumed, not invested). Correct? Perhaps I get it now?

Or put the question this way: if one never *invests* any of the consumption dollars in the trajectory, do those future consumption dollars still have a *present value* that exceeds their face value in any given year? If so, how did they get this extra present value? And if not, then why use use present value of consumption dollars as a way of ranking the trajectories?

Again, perhaps their present value is greater than their face value because future consumption dollars are a product of other investments even though those investments themselves didn't come from the pool of consumption dollars?

--Dan

3

2032 74 80 58,858 34,145 37,028 41,447 46,155 60,159
2033 75 81 61,683 35,170 35,930 40,694 47,310 59,380
2034 76 82 61,606 34,711 34,908 38,047 46,404 55,639
2035 77 83 61,528 34,505 34,464 38,008 42,885 51,722
2036 78 84 61,449 34,284 38,627 40,718 46,100 56,849
2037 79 85 61,368 36,616 38,102 41,691 47,817 63,510
2038 80 86 64,076 38,382 39,840 39,307 53,017 65,693
2039 81 87 64,096 36,235 48,319 48,797 64,056 66,168

Here's a section from my "Trajectory Living Standard." You know the column headings. Notice year 2035 and 2036. Do I read this by saying: OK, in even the highest rank trajectory, I wouldn't meet my "recommended" trajectory? Since that last column represents the 95th lowest (I assume that means 95th percentile of the group of 500) then I just assume that this is ok and that I'll make up for it in the following years where those numbers outpace my recommended trajectory? Where a column of numbers lags behind my corresponding recommended trajectory, does that mean I should applaud that my recommended trajectory is higher than most of the columns? Or does that mean that I should worry and adjust things so that the recommended trajectory is more in line with at least the medium case scenario?

Is my "recommended" trajectory as the mean or avg, a possibility? What does this table really tell me?

I'll call Larry next week, but I thought he or someone might have some quick words on this question.

Dan

4

Dan,

When you have Monte turned on, the "recommended" trajectory shown in the Main and Detailed reports is generated assuming you earn each year the mean return on your assets that you tell the program you'll be holding in that year. So it's showing what you'd be able to consume and accumulate each year were you to know for sure you'd be earning on your assets what you can expect, but can't be sure, to earn.

The Monte trajectory reports is showing you particular paths that your liviing standard and other economic variables can take as you age. The 95th percentile trajectory is showing you what happens along the path that has the property that, OVER YOUR LIFETIME, your total lifetime consumption (measured in present value) is 95th highest compared to teh LIFETIME CONSUMPTION of all other trajectories.

The point of displaying these trajectories is to indicate that even though you may do well, on average, with respect to the returns you earn over your lifetime and end up with a very high level of lifetime consumption, you'll experience a lot of variability in your living standard along that path from year to year because your returns will be high in some years and low in others (even though they'll generally be high).

In a nut shell, they say that doing well (poorly) over your lifetime with respect to the returns you earn, doesn't mean you'll do well (poorly) each and every year.

best, Larry

5

Dan,

When I gave my example of a present value in my prior message I was making a general point about present values.

The present value Y of an amount of money, X, received n years from now is given by

Y = X divided by the quantity (1+r) raised to the power n, where r is the annual return you can earn on the money you invest.

best, Larry