MonteCarlo Project Management Assingment Help With Solution
1. What is the geometric annualized return for stocks, bonds, and a balance fund since 1926?
_______________ and ______________ and ______________
2. Look at the monthly standard deviation for stocks. What did I do to annualize that number for cell C11?
3. What is the apparent relationship between return and risk as measured by the standard deviation?
4. Let’s calculate the VAR for any given year using the Geo. annual return for a balanced fund and its annualized standard deviation. Assume you invest $1,000. What is the 95% VAR? Don’t know how to do this? Look at my Powerpoint. There is a great example there. Use Cell H9 for the return, E11 for the standard deviation.
VAR = ______________________
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- Click on the Theory sheet. This will tell you how much you can expect to have and give you a lower and upper limit over time. You cannot simply add and subtract a standard deviation which you can do for any given year since compounded returns are lognormally and not normally distributed. However, I have developed a model that can do this (Trainor 2005, for those who really love finance). Given our numbers we found earlier, let’s plug in 12*the monthly average return for stocks(Cell C9) in Cell B6 in the Theory sheet, and the annualized standard deviation for stocks which goes in the Std. Dev. row The table looks like this but note these are not the right numbers.
|Expected Return =||10.00%|
|Std. Dev =||18.00%|
Set the confidence interval at 80%, set the beginning value to $100 and the annual payment to $1,200. Thus, we will find how much we are likely to end up with assuming we invest 1,200 each year.
At the end of 30 years, what does the following say:
Expected value = _____________ Lower limit =____________ Upper limit equal = __________
Lower limit annual return = __________ upper limit annual return = ____________
- Let’s go back to the MonteCarlo sheet. Hit the F9 key a few times. What do you see happening? You should see numbers change. In Cells C3 and C4, make sure $100 is there. We are going to hit F9 10,000 times and see how much investing $100 every month for 30 years is likely to accumulate to based on historical returns and standard deviations for a stock, bond, and balance fund. We just did this in our Theory sheet by starting with $100 and having the annual payment = 1,200 since it goes by years. However, it will be slightly off because we are investing monthly, and not yearly. The values we end up with will be different because of this, not tremendously so, but certainly won’t be near exact. Also, the great thing about Monte Carlo, we can actually go to the MCResults and find out what happens every time.
Now how do we perform Monte Carlo simulation? One way is to hit F9 10,000 times and write down the values in Cells N10, O10, and P10, but that might take awhile. Instead, hit that big Monte Carlo Macro button. Excel will do it for you. Now I’m not the most efficient programmer, and Excel is not very fast anyway, but before you complain about watching the blue circle of death for a couple of minutes, keep in mind, the other option was hitting F9 10,000 times.
Interested in the Macro, click on the Developer Tab and click on Macros. You can read the code there. Don’t have the developer tab? Click on the office button, top left, click excel options, there is a box that states, show Developer tab in ribbon. Check it. Depending on Excel version, this may be in different places.
At this point, probably best just to cut and paste the table under the button. There are a couple of questions I’m going to ask about it in d2l.
Make sure you know what formula I used to create random returns in columns K, L, and M. This is handy to know. It basically samples from the Normal distribution based on a mean and standard deviation input.
Thus, this takes care of questions 6 and 7.
Now that we know how much we may end up with, let’s go see how much we can spend.
Part B: After Retirement
Click on the AfterRet sheet. Here you will see a yellow box. Looks like this:
|Withdrawal Amt.||5%||Monthly =||$416.67|
|Expected Annual Ret||4%||Monthly =||0.33%|
|Annual Std. Dev.||10%||Monthly =||2.89%|
|Annual inflation rate||2%||Monthly =||0.17%|
|Ending Amount 25 yrs||$0|
|Ending Amount 30 yrs||$0|
Let’s start with $100,000. Set the withdrawal amount at 5%. This is based on a general rule of thumb that states you can withdraw 5% and increase the fixed amount by the rate of inflation. Thus, your initial monthly payment will increase by the rate of inflation. The idea is that this withdrawal rate should see you through retirement. Keep in mind for married couples, there is a 50% chance that one person reaches the age of 90 and 18% chance one makes it to 95. Thus, we may want to make sure we have funds for almost 30 years if retiring at the age of 65.
Let’s find out what we can withdraw. To answer the questions below, use 10,000 simulations. You can probably get away with 5,000, but standard practice is at least 10,000. Due to my inefficient programming skills, (blame Excel too), you may have to wait a couple of minutes if you use 10,000.
8) Using a 5% withdrawal rate and assuming a 5% expected return, 10% annual standard deviation, and 2% annual inflation rate, what is the probability you will not run out of money for 25 years? 30 years?
________________ and _______________
9) Using a 6% withdrawal rate and assuming a 5% expected return, 10% annual standard deviation, and 2% annual inflation rate, what is the probability you will not run out of money for 25 years? 30 years?
________________ and _______________
10) Using a 6% withdrawal rate and assuming a 5% expected return, 10% annual standard deviation, and 2% annual inflation rate, how much money can you expect to have leftover for your heirs after 30 years? Use the median value for this.
Median remaining value = _____________
Now you may know why 5% is used. Much higher is a bit dangerous. We could try to make more money although that will likely come with more risk. You can try some different combinations but I would move the simulations back to 1000. I have add in programs that are much faster than my Macros but they do not work with all Excel versions. If you like this type of analysis, try the Poptools add in. It does a nice job for simulation.
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