[ Music ] >> So, up to this point, we've done some general examples with various assumptions for large stocks and small stocks and the risk-free rate. I thought it'd be nice to just like kind of go to a real-world application here of efficient frontiers and dominated assets. And this is a real-world example which can literally save you, potentially here, tens of thousands of dollars. No joke. OK? I'm serious here. So, let's-- you know, I'm sure you're intrigued now, so now's a great time to have a question and this is something if you're holding one of these dominated assets in your portfolio, if you get rid of the dominated asset, you maybe have enough money saved that you can actually visit this guy for real as opposed to just seeing him on all these question slides. So, what's the question? Let's go to the tablet here. In the real world, maybe somewhere in your own portfolio, is there a classic example of a dominated asset? This may be an asset that you're actually already holding. So, in the real world, what's a classic example of a dominated asset, dominated security, one that you may even be holding in your portfolio? Alright. So, I'm sure at this point you're kind of very intrigued about what's the answer and then, you know, should I buy my plane tickets to Paris to see Le Penseur? So, I have said-- I've been to kind of Paris, you know, multiple times and it is worth seeing. Maybe not on day one, two, or three because there's so many cool things in Paris, but, you know, maybe on day four or five to check it out. But, first we need to be sure we're not holding this dominated asset so we have more money in our account when we retire so we can do this trip. So, what is the, you know, kind of answer here? A classic dominated asset in the current finance world would be a mutual fund that has the same underlying assets as another mutual fund, but charges a higher expense. Let me give you a classic example. S&P 500 index fund. So, different mutual fund companies offer different S&P 500 index funds and when we're talking about S&P 500 index funds in the US, think of it covering, you know, kind of 500 roughly largest companies. So, if you're investing in the S&P 500 index fund, you're coming pretty close to kind of mimicking the overall market. You're missing some of the small cap stocks, but you're coming pretty close to mimicking the market. So, let's look at this example here. Two S&P 500 funds. One has an expense ratio of .05% per year or five basis points. The other has an expense ratio of 0.4% per year or 40 basis points. And both of these products exist in the marketplace. I won't mention any names, but, you know, you could do your research and find them here. So, the question is, suppose we're invested in fund A, S&P 500 with the low expenses. Fund B, S&P 500 index with the higher expenses. How does that affect our wealth and our portfolio? OK. And to do this calculation, we need to make some assumption about what's the underlying return of the assets in the fund, the S&P 500. So, let's assume that that's growing at 10%. So, the question is what is the difference in wealth if you've invested in fund A versus fund B if you have a holding period of 10 years, 20 years, or 40 years. So, when you're thinking of 20 or 40 years, think about this as an asset in your 401k defined contribution retirement plan. So, that's why I think this is kind of a nontrivial example because, you know, you're probably investing a lot of your wealth, retirement savings, in such a setting. S&P 500 index fund may be one of the options, so you would like to see, hey, is this a high cost or a low cost expense and what makes fund B a dominated asset in this case is it's exactly the same as fund A, the only thing that differs is the expense ratio, which will just mechanically lower the after fee returns. So, let's go through the example here and crunch the numbers. So, for fund A, the return per year-- instead of 10% is pretty close because you have to deduct that fee, 9.95%. And we do that for 10 years, so that goes up to 2.58. OK. We're assuming you invest a dollar here if you want to make this 1000, 10,000, 100,000, just multiply through here. For B, we're also earning this 10% return, but that is actually 9.6% after we deduct the fee. So, after 10 years, this is 2.5. So, A to B, OK. Your wealth, if you invest in fund A, you hold it for 10 years, 3.2% higher than if you've invested in fund B. OK? But, you're probably not investing a dollar, you're maybe investing 10,000, 100,000, you know. Who knows? Depending upon your financial situation. How about if we expand for 20 years? OK. And I won't go through the, you know, kind of compounding calculation explicitly here. I'll let you do that. I'll just give you the final result. Then the difference in wealth is 6.6%. The wealth in-- for the person investing in fund A, 6.6% higher if there's a holding period of 20 years than for fund B. How about if it's 40 years? So, think of a scenario where you start saving for retirement at age 25. You hold that investment for 40 years. You retire at 65. How much money do you have? You're ready to do your trip to Paris to see Le Penseur, a statue by Rodin. So, you have 13.6% more wealth if you invested in fund A than fund B. So, I don't know if 13.6% seems a lot or a little, but if your final balance is a million in fund B, it would be 1,136,000. In fund A you'd have an extra $136,000. You can do, you know, trips to Paris, you know, every year for a while anyway. And it's just simple. A and B are exactly the same, both are S&P 500 index funds. A charges five basis points per month, .05% expense. B charges .4%. I say-- I said .05% per year, five basis points for fund A. For fund B, .4%, 40 basis points per year. Seems like a very small difference and over the 10 year horizon, maybe it is not that big a deal, 3%. But, I would ask why shouldn't you have the 3%, given the underlying assets are the same. Once you go out 40 years, it's real-- the difference is really starting to compound. Now, let's do another example. This is more dramatic, but also kind of more controversial, I guess you could say, because now we're not exactly comparing orange versus orange. We're really comparing maybe orange versus tangerine. OK? So, we're talking about index fund investing in equities. Think of John Bogle at Vanguard versus active managed equity funds. And it's well documented the expenses, the fees, for actively managed equity funds-- so, this is a stock fund where the manager is making stock picks. They're not investing in all the stocks in the market, they're not just holding the members of the S&P 500, they're not doing a buy and hold strategy, they're making active bets about which stocks are going to go up more than others. OK. So, because of that trading, because of the time they spent looking at the portfolio, you have to pay a higher expense for these actively managed funds. Now, the evidence is these actively managed funds don't outperform the index funds before expenses, let alone after expenses. So, let's look at an example here. We're changing it up. Now the change in expense ratios is going to be different. Much greater than it was before. So, S&P 500 index fund A, that's still around. We like this five basis points per year, .05% per year expense ratio. Now we're comparing it to an actively managed large cap fund, like the S&P 500 is large stocks, so actively managed large cap fund. It has an expense ratio of 1.25% per year. So, think of this as a fund that was bought through a financial advisor, which generally will add fees to opposed you bought the fund on some mutual fund company website. OK. So, you're buying this through an advisor. So, now your fees are 1.25% per year. Again, not in implausible example. I know, you know, plenty of people at some point were invested in such funds as fund B. Let's assume that both the S&P 500 and the large cap fund have a 10% return each year. So, this is where the controversy comes in. So, the large cap fund manager may say hey, I'm going to beat the market. I'm going to generate 12% per year. That's why I'm charging a higher expense. So, that may be true, but the evidence in general says that generally doesn't turn out to be the case, that basically the, you know, the actively managed funds aren't beating the market. So, let's just assume that both of these funds generate 10% return before expenses. How do the fees compound? How do they affect wealth? OK. Again, let's look after 10 years, after 20 years, after 40 years and see the difference in wealth accumulation for fund A, the S&P 500 index fund low cost, fund B the actively managed large cap fund with a high expense ratio, but not, you know, unusually high if the fund is being bought through a financial advisor channel here. So, how do these differ 10 years out, 20 years out, 40 years out? So, at 10 years out, we already did this calculation for fund A. Instead of 10% per year, after expenses it's 9.95% per year, but pretty similar. And we know this equals 2.58 for a $1 initial investment. How about fund B? Now, here is where the expenses really come to the fore. Here, let me do a better job. That 10% return before fees is only 8.75% after fees. So, even after 10 years, you have 11.6% more wealth if you had invest in fund A as opposed to fund B. Just after 10 years. Now, you can see where this is going. What if we take it out a 20-year period? Or a 40-year period? Think of a 40-year buy and hold investor. You invest when you're 25. You take the money out when you're 65. OK. So, for 20 years, the difference between the two, almost 25% higher balance if you had invested in fund A than fund B. And how about if we go out 40 years? Over 50% higher balance. So, in other words, if you had invested in fund B, the actively managed fund with the 1.25% percent expense ratio each year, let's say your balance had grown to a million dollars 40 years later, your balance with fund A would be over $1.5 million. OK? So, that I think deserves a wow. But, what is the assumption here, in fairness, that both the index fund and the actively managed fund are generating the same return before expenses, so then the active managed fund is like-- both are running a 50-yard dash, but the actively managed fund is starting like five yards behind the index fund. It can't catch up. In my assumption, I don't allow it to catch up. I'm assuming the returns are the same. The active managed fund manager may argue that I'm charging a higher expense, I'm going to deliver a higher return, you know, before expenses to compensate for that. Although, the empirical evidence suggests, on average, maybe not in every case, but on average that doesn't seem necessarily to be the case. So, kind of bottom line to take from this lesson is if you're investing in a certain fund with a popular objective, let's say it's S&P 500 fund, let's say it's a NASDAQ growth index fund, be sure you're investing in the fund with the lower expense because if you're paying a higher expense when there's other funds that have exactly the same underlying asset, but the charge a lower expense, you're just throwing money away and you're invested in a dominated asset, which you don't want to do.
