 Welcome to the session. This is Professor Farhad in which we will work an example that deals with rate of returns, computing the arithmetic rate of return, geometric as well as the dollar weighted average. Every time I say the word example, it means I already explained this topic in a prior session much, much more in depth. So if you want to look at the detailed explanation, please do so before looking at this example. This topic is covered on the CPA as well as the CFA exam, Essentials or Principles of Investments. As always, I would like to remind you to connect with me on LinkedIn. If you haven't done so, YouTube is where you would need to subscribe. I have 1,700 plus accounting, auditing, tax, finance as well as Excel tutorial. If you like my lectures, please like them, share them, put them in playlists. If they benefit you, it means they might benefit other people. Connect with me on Instagram. On my website, farhadlectures.com, you will find additional resources to supplement this course as well as your accounting and finance courses. Check out my website. So to illustrate those concepts, arithmetic, time-weighted and the dollar weighted average, we're going to be looking at this example. The funds begin with the 10 million dollar and reports the following monthly results with negative figures and parentheses. So we started with 10 million, we invested in the fund 10 million and this is what happened. The first month we earned 2% and the investor spur in 300,000 dollar. The second month, we earned 8% and we added half a million dollar. In the third month, we had a negative return of negative 4% and the investors had not put any money. The question becomes compute the arithmetic time series and the dollar-weighted average. Let's do real quick the arithmetic because it's the simplest one, 2 plus 8 minus 4 divided by 3, 2 plus 8, 10 minus 4, 6, 6 divided by 3 equal to 2%. Simply put, we just computed the arithmetic and we earned 2%. Now, let's compute the time series or the geometric. Time series is the same thing as geometric. How do we compute this? It's 1 plus 0.2 times 1 plus 0.8 times 1 minus 0.4, which is technically 0.6. We raised all of this 1 to the third tower because we had three periods. We subtract 1 and we get to the answer and the answer should be less than 2%. If the answer is more than 2%, then we have an issue. You did something wrong because the time series or geometric should be lower than the arithmetic. Now, let's go to the Excel sheet to compute because I prefer that you do it in an Excel sheet, the geometric, than we would look at the dollar-weighted average. This is the data that we are giving. Let's first commute the arithmetic just using Excel sheet. This way, I want you to also make sure you are comfortable with the Excel sheet. Basically, you would pull the average, the average function, you highlight the numbers and it's going to give you 2%. Now, let's compute the geometric. Again, the same thing. You put all the returns, the 2%, the 8% and the 4%. Then you pull the geomine formula and basically, you will take geomine equal geomine and let me just pull the formula in front of you. Basically, you will go to the geomine. You highlight the numbers and you add 1 plus 1 on the n17 not n18. Then what you do is you take this number minus 1 and you'll take the answer minus 1 and let's see what the answer is. It should be less than 2%. It's 1.88. Again, in the prior session, I explained to you what does 1.88 means. This is the geometric mean. This is the geometric mean. This is the arithmetic mean. Again, this is 2%. 1.88 is less. It means if you invested your money somewhere else, you would end up overall with 1.88% in three months versus this fund. We did the arithmetic. We did the geometric. Now, we need to do the dollar weighted average. To do the dollar weighted average, we need this data again. Here's the data. We started the beginning of the month we had. We invested with 10 million. Then this 10 million made a return of 2%. What does that mean? It means I made $200,000, which is 10 times 0.02. Then the investor brought in $300,000. Let me add the $300,000. What did I end up with? They brought in $3,300,000. I made $200,000. They bought $3 million. I end up with $13,200,000 the first month. The second month, I started the second month with $13.2, which is the ending of the first month becomes the beginning of the second month. The rate of return is 8%. I'm going to take 13.2 times 8%. That's going to give me a growth, a return of $1,056,000. Then the investors brought in $5 million. That's pretty good. The investor brought in $5 million. I end up the second month with $19,256,000. Now I'm going to start the third month. The third month is basically what I end up the second month, which is the 19.25 million. I lost 40% of this. I'm going to take this. I lost 40%. I'm going to take this multiplied by .4. I lost $770,000. The investors did not bring in any money. They panicked. They did not bring in any money. Therefore, I end up with $18,480,000. This is what I end up with. This is what I started with with $10 million. Basically, this is my growth. This is what I earned and I lost. This is what the investors put in. I end up with $18 million. Now, once I have this information, I'm ready to compute my IRR. Remember, I have to turn this into a problem. How do I compute my IRR? I just turn it into a capital budgeting problem. At period zero, this is the period, period zero, I invested $10 million. At the end of period one, I invested another $3 million. Again, when I invest, it's negative, so this is the $3 million. Period two, the investors brought in, or I invested $5 million. At the end of period three, nobody brought anything. Therefore, it's zero. Therefore, it's zero. But I cashed out. I cashed out. It means I walked away with $18.4 million. So this is positive. So year three is positive. Now, I'm ready to compute my IRR. So basically what I would do, I would go to my function, since it's finance. Let me just bring down the finance. Let's go to my IRR, compute my IRR, the values. Let me just compute the values right here. Here are the values. Let's go to IRR, internal rate of return. And the values, these are my values. And click on OK. I'm going to show you the formula. So on a weighted average, a dollar weighted average, I earned 1.17. It's even lower, lower than the arithmetic and lower than the, than the geometry. Because remember, the arithmetic was 2%. The geometric was 1.88. The arithmetic is lower. Why? Because although I made, although I made 2% and in one year 8%, but when I suffered the 40%, I had almost 20 million. A lot of money invested and I suffered a lot all at once. Okay, so that's why it's not my, my dollar weighted return is not as good as 1.17. Once again, as I mentioned in the prior recording, mutual fund, they quote the geometric mean. Geometric mean, geometric mean over the three, over the period. Why? Because the geometric mean don't take into account the dollar amount because the mutual fund manager cannot control whether the, whether, whether the investors take money out. They have no control over that. All that they have control of is how well they invest the money. As always, I'm going to ask you to like this recording and share it. And in the next session, what I would do, I'm going to look at APR versus EAR, annual percentage rate versus the effective annual rate, which is the convention for annualizing rate. As always, also I'm going to invite you to visit my website for headlactures.com for additional recording, for additional recording and more practices. If you are looking to increase your knowledge, improve your performance. Good luck, study hard and stay safe.