John Luskin: Welcome to the 59th edition of the Bogleheads on Investing podcast. Today our special guest is Dr. William Sharpe. I'm John Luskin and I normally host our Bogleheads live show for the folks of Twitter. I'll be taking over for the normal host, Rick Ferry, while he takes a summer sabbatical.

Please allow me to introduce Dr. William Sharpe. He was one of the originators of the capital asset pricing model, developed the Sharpe ratio for investment performance analysis, and developed other methods for the evaluation of options, asset allocation optimization, and investment return analysis for evaluating the style and performance of investment funds.

Dr. Sharpe has published articles in a number of professional journals and is a past president of the American Finance Association. In 1990, he received the Nobel Prize in Economic Sciences for his work on the capital asset pricing model. You can learn more about Dr. Sharpe at wsharpe.com. Some announcements before we get started on today's episode with Dr.

Bill Sharpe. This episode of the Bogleheads on Investing podcast, as with all episodes, is brought to you by the John C. Bogle Center for Financial Literacy, a nonprofit organization that is building a world of well-informed, capable, and empowered investors. Visit boglecenter.net where you'll find valuable information, including transcripts of podcast episodes.

Another announcement, registration is currently open for the 2023 Bogleheads Conference. This year's conference is on October 13th through the 15th in Maryland. We have some phenomenal personal finance and investing rock stars who will be attending as speakers, including Charles Ellis, Paul Merriman, Clark Howard, Jonathan Clements, Michelle Singletary, Barry Ritholz, Wade Pfau, and more.

And of course, Bogleheads favorites, host of this show, Rick Ferry, Christine Benz, Dr. Bill Bernstein, Mike Piper, Alan Roth, and much more. Go to boglecenter.net/2023conference to see the full lineup and to register. Also, you still have time to take advantage of the discounted room rate. Again, that's boglecenter.net/2023conference. And finally, a disclaimer, the following is for informational and entertainment purposes only, and should not be relied upon as investment advice.

And with that, let's get started on our interview with Dr. William Sharp. Bill, welcome to the 59th Bogleheads on Investing Podcast. Thank you for joining us. My pleasure. In 1990, you jointly received the Nobel Memorial Prize in Economics with Harry Markowitz and Martin Miller for your work on the capital asset pricing model.

Tell us about the capital asset pricing model. The idea is that the more securities you have in a portfolio, the less important is the risk that's specific to a given stock, whether it be from the company's activities or from the industry it's in. So as you put more and more securities in a portfolio, what we call idiosyncratic risk, the risk that's attributable to the fact that General Motors or the fact that it's in the auto industry, that risk tends to be diversified away.

And as you diversify more, the risk in your portfolio becomes predominantly due to what's going on in the broader market. So certainly Bogleheads are fully subscribed to this. We love diversification and we love those low cost index funds. We want the return of the market. We're not necessarily putting all our money into just one individual stock and that helps manage risk.

Let's jump to one of our questions that we got from Twitter. This question is from a user named Levi who writes, "Do you still fully subscribe to the capital asset price model?" Well, it's a model and models abstract from reality in various ways and get results based on what goes into the model, what you assume in the model.

The CAPM, the original version in the dissertation assumed that all stocks had risk that came from "the market" and then idiosyncratic risk that was unique to them and not correlated with anything else going on. So in that sense, it assumed, it was not perhaps surprising I got the result that expected returns would be related to beta values, that is sensitivity to the market.

The broader model used just the idea that the more diversified your portfolio, the greater would be the component of risk in that portfolio that was attributable to the market as a whole. And so in a sense it did not assume that the market was the only source of returns.

It in some sense got bad results that the market portfolio was predominantly, I should say to be careful, the risk for which there would be rewards and higher expected returns. There was a radical difference between the two. And some people who knew the first were, had thought that the second result, the CAPM resulted from assuming the "single index model," that is that only market risk was the correlated risk in securities, it did not.

Again, if you have enough stocks that will diversify away and be of much less importance and therefore not rewarded, the non-market part would not be rewarded in higher expected returns. This question is from David from Twitter who writes, "It would be great if Dr. Sharpe could comment on CAPM assumptions and the degree to which the model's value has changed as markets have evolved." It's hard to describe to somebody in today's world how irrelevant the stock market was for most human beings back in the 50s and 60s.

Relatively few people had individual stocks, there were not 401k plans, and there certainly weren't as many securities as there are now, or as many different exchanges, et cetera. At the time, the idea was that the market as a whole could be sufficiently dominant in expected returns that it would be a high, high, high percentage of the influence on expected returns.

Now there was the idea that only the beta of a security would have an impact on its expected returns. That was a pretty far out assumption. Now there are so many securities, so many markets for that matter, and so many people who own securities that nowhere else in their 401ks or 3Bs, I think it's to me at least a more comfortable assumption.

Let's jump to measuring risk next. This question comes from username 95 suited from the Bill Bled's forums who writes, "Should investors consider volatility to be the primary measure of risk when constructing financial portfolios?" I would say yes, if they have a bunch of securities or a mutual fund that has a bunch of securities or multiple mutual funds.

Obviously, if they have an investment portfolio of three stocks, there's a lot of non-market risk in that portfolio. But if they do what bobbleheads might, by and large, I would assume do, yes. Yes, certainly. I wonder if 95 suited is referring to some other risks that long-term investors might face, such as inflation risk.

That's to say, if you don't want to take volatility as a risk, the risk that your investments decrease in value, then you're not necessarily getting rid of all risk so much as you're trading that one risk, volatility, for another risk, which is inflation. If you're not going to invest in assets like stocks that have historically grown more than inflation, then you might be looking at your wealth decreasing over the long term.

Well, I think there's a very strong argument that for most people, the returns that matter are real returns, inflation adjusts. Now, you know, we can talk about how important is inflation for old people versus young people, but in a sense, I would favor thinking of returns not as nominal returns, but as real returns.

Pick your country and time period. Inflation may be dominant. It may, if you're lucky, for a short period in some countries be sort of minimal, as we well know and as we're experiencing. In most countries, in many times, inflation is important. So in some sense, it's easy to just do everything in real returns.

When I'm doing projections, Monte Carlo, what have you, I tend to like to do it all in real returns. Then the literature, there's an argument that for retired people, inflation may not be quite as formidable a factor, depending on if they've bought their house and they paid off their mortgage, et cetera.

Retiree taxes in some places in California, for example, there's a limit on how much they can be increased once you bought the house, et cetera. My inflation may be different than your inflation. There's some research by David Blanchett that talks about the spending smile of retirees, showing how retiree spending might not actually keep up with inflation.

I will link to that in the show notes for our podcast listeners. David Blanchett, by the way, was our guest on episode 14 of the Bogleheads Live show. I'll also link to that in the show notes. Let's talk more about measuring risk. This question is from the White Coat Investor from the Bogleheads forums, who writes, "Risk adjusted return calculators, such as the Sharpe ratio, use volatility as a measurement risk.

Volatility is the change in price of your investment." The White Coat Investor goes on to say, "A long-term investor really shouldn't care much about volatility. Does that mean that they shouldn't care about the Sharpe, Treynor, or Sortino ratios?" And before we answer that question, perhaps you can tell us what those ratios are.

I can probably answer that part, what the Sharpe ratio is. And let me say, by the way, I didn't call it that. I called it the reward to variability ratio, and I think it was Gene Fama started calling it the Sharpe ratio. The idea of the Sharpe ratio is to at least take two things into account, you know, an average returns and a standard deviation.

Standard deviation, for those who aren't investing nerds, is just a way that we can measure risk. How much our portfolio changes in value. This is the same thing as the volatility that we just mentioned. Standard deviation, volatility, and risk are often all used interchangeably. The T statistic or the Sharpe ratio, it gives you credit for higher average returns.

That's on the top and it gives you a discredit or demotes your number or lowers your number for more risk, more variation. That's the number on the bottom. And so this has in the numerator an average and on the denominator a standard deviation. So you get a better number if you do better on average and you get a better number of the things equal if you have less variability.

It's not unlike a statistical measure called the T statistic, which again is saying, well, here's how you did on average, but how much variation was there? If you did this on average and it was almost the same every single period, then using that number as a prediction makes me more comfortable than if it was that on average, but it was very all over the place.

The original idea, as you know, it takes into account the risk-free rate. So it's not just the average return on the top. It's average over and above the risk-free rate. That's because it assumes that you can borrow and lend at that rate. And so you could take that portfolio and lever it up or down at that rate.

That's the economics behind it. The Sharpe ratio, it's a useful number. I would not refuse to look at it if somebody offered it to me for an investment. And again, it's particularly important to understand that for a piece of a portfolio, the risk of that piece may or may not be important depending on how correlated it is with what's going on with the other securities in the portfolio.

I sometimes say when people ask about the Sharpe ratio, they say, look, folks, we have computers now. We don't need to put everything in one number. We can look at more than one number, you know, what was the average return and what was the risk and what was the beta, et cetera.

We can do things that are more sophisticated. I serve on nonprofit investment committees. Very often the consultant or the manager will show you Sharpe ratios for every investment in the portfolio, this fund, that fund, et cetera. That doesn't really help you much with what it was originally intended for.

It does help you in the sense it's like a T statistic. It is interesting if a manager did not only well, but did it with quite some consistency. You have more reason to believe that you'll might get some good results in the future. Like some manager who is touting a Sharpe ratio, I don't know, it was five or something, you know, this humongous Sharpe ratio and looked at it and said, it was based on, I think it was 14 monthly returns for private equity for which there was no market value.

It was just an estimate. And they'd put down these 15 estimates and sure enough, there wasn't much variation and they've done all right, according to the estimates. So sometimes there are uses that I would not endorse. For those folks who aren't investment nerds, why that is hilarious for two reasons.

Number one, a 14 month investment return is pretty much random. And then also if it's a private investment, the manager can pretty much make up whatever price, whatever investment return. What do you want? What would you like it to be worth? All that's to say how they use the Sharpe ratio in that situation is quite silly.

And then for me, the Sharpe ratio is very special because I looked at how endowments did next to index fund portfolios for a master's thesis. Hey, what happens with $600 million to invest? Well, the data already exists to show that those endowments would have been better off with low cost index funds.

But what about risk? What is the risk adjusted return? So I use a Sharpe ratio and the Sortino ratio to show even on a risk adjusted basis, considering how much risk you are taking, that the amount of return you're getting compared to that index fund portfolio is not that great.

And of course, if you're comparing portfolios and you can borrow and lend at the riskless rate, then the portfolio with the highest Sharpe ratio is golden because with leverage up or down, that can beat anything below it. Let's jump to the second part of the White Coat Investors question who asks, "How can we adjust for the deep risks discussed by Dr.

Bill Bernstein, such as inflation, deflation, confiscation, and devastation?" Let me maybe twist the question a little to a broader question, to what extent is it useful to look at historic returns on a security portfolio, the market, whatever, as a predictor of future returns and risks? And that's a very serious question you have to ask yourself.

I would say, I think it's incumbent upon you or your advisor to look at history to see how that particular portfolio would have done in the past. I don't think you should say past is not a predictor of the future, so don't look at all. On the other hand, if a portfolio did well in the past, how likely is it that it's going to do well in the future?

And I would say generally not very likely. Risk is a somewhat different matter. Past risk is probably a better predictor of future risk. In an efficient market, past expected returns that are abnormally high are unlikely to be repeated as are terrible returns. If it's done really well in the past, the market knows that, and the price reflects that to the extent that it's predictive of the future.

So don't expect, with any kind of certainty, abnormally high returns in the future. Let's talk a little bit more about the risk-adjusted metrics that are out there. Username Chiggy from Twitter writes, "I should ask him if the Sharpe Ratio is the best risk-adjusted return metric to compare index funds versus mutual funds." In principle, the Sharpe Ratio should be used for your whole portfolio.

In many cases, it's used for pieces of the portfolio. It's useful, but in a different sense. And if you're using it for pieces of a portfolio, then it's more in the sense of the T-statistic. How did that piece do on average, and how much risk variation was there getting to that average?

If you got that average return almost every single month, then that's a very different story than if you got it ranging all over the place. For a whole portfolio, don't just use the standard deviation. Look at the whole distribution. How many months, let's say, over the last 20 years, did it lose 20%, did it lose 19%?

Show the range of things that happened and how frequently they happened. That's for the whole portfolio. For pieces of the portfolio, even standard deviation, the typical risk measure, standard deviation of a portfolio of X plus Y is not just the average of those two standard deviations. It depends on how they move together, so it gets more complicated.

Thoughts on the Sortino ratio? My recollection is that for the Sortino ratio, for the risk side, uses downside risk on the grounds that the risk of that you'll do better than expected doesn't seem to be something you should worry about. And Sortino is certainly right. When you're looking at a whole portfolio, what you care about is downside.

Outside risk is fine, you know, the more the merrier. And there's the issue, if the distribution is symmetric around a middle point, you know, when you plot it, it looks sort of the same on the downside as on the upside, then it kind of doesn't matter whether you use standard deviation or the standard deviation of the downside.

Bill, I mentioned earlier that I used the Sharpe ratio to compare index fund portfolios to the very high fee portfolios of endowments to compare their performance on a risk-adjusted basis. I also used the Sortino ratio and the results were very similar. That's kind of my expectation. The probability distributions aren't symmetric, but they're typically of a similar enough form.

Probably if you rank on one, probably rank on the other. This question is from username Derrick Tinnin from Twitter, who writes, "Are the persistent flows to index funds changing the market structure?" I guess there are two ways of looking at that question. One is, were there not those funds, how different would things be?

The other is, given there are those now and there were not back in my early days, how different are things, and I'll skip the latter one because the world is so different in general. I don't even know how to start on that one. I guess one difference if people generally stop using index funds would be they'd be poorer because they'd be paying higher fees.

And as Jack Vogel has wrote about and talked about many times, that's not a trivial difference. That's a major difference. Some of the ironies of efficient market theory broadly construed is there's a sort of a contradiction. We assume that people are really working hard to figure out exactly how much more General Motors is worth than General Electric, and that all those prices take into account information in very efficient ways.

And yet we encourage investors to pay no attention to any of that and just call them all. And there has to be a point at which there aren't enough active managers, people doing research on securities to keep the market prices right, as it were, to incorporate the information that's extant into security prices.

That's a really interesting thing to worry about. And over the many years since we all started in this field, question is how much indexing is too much? My hope at least is that if and when we got to that point, enough people will peel off and start doing security research and become active managers.

Where that point is, I don't know, but it is a dilemma. So you don't want to convince too many people to index. Unfortunately, the people who don't index are paying the price for that research through higher fees. It's a very strange kind of equilibrium. Do I worry about it now?

No. Do I index now? Yes. When I started teaching the investments course at Stanford, and this would have been 1970 or thereafter, I would start the course by going into the classroom and writing on the board a phone number. And I would say, this is the most important information you're going to get in this course.

And I'd wait for somebody to say, well, what is that? And I said, that's the new customer line at Vanguard. This is true. And I'm making this up just to please the Bogleheads because they were at that time the only place you could get an index fund. It's an issue to think about, if not worry about, is there too much indexing?

The answer is no, but I can't prove it. Certainly to your point, if too many index fund investors means an opportunity to make some money, someone's going to try and do just that. Of course. And the question is, how much, if any of that, will the managers pass through to the shareholders of the fund?

To quote Rick Ferry, if there is any alpha, it goes to the managers. Let's move on to another question on index investing. This one is from username SB1234 from the Bogleheads forums who writes, are buy and hold index fund investors free riding in the sense that they do not contribute to price discovery?

I think so. There are certainly managers who get rich by being in some sense superior in getting information and acting on it. I have a general audience teaching the investments course at Stanford and I will divide them into two halves, left side of the room, right side. They're all money managers in this market and they collectively are the market.

I would assign half of them to be index fund managers and tell them what they did. They had to figure out how many shares were outstanding of each and by exactly proportional amounts and the people on this side were active managers and I would describe this one does research on this and that one does this and, you know, give them a sense of what active managers do.

So I'd say these folks own half the market and those folks collectively own half the market and the index managers, of course, each of them owns the same portfolio, but the active managers are all over the place. And then I would say, okay, before costs, the market is down 12%, okay, before costs, what did this passive manager earn and they've said 12%, what did that one earn, yeah, 12%.

Now over here on the active side, what did this one earn, 30%, brilliant, what did this one earn, minus 12, what did the average dollar earn on the passive side before costs and they think a bit, 12%. What did the average dollar earn on the active side, it takes a little while, it gotta be 12%.

Okay. Then we take costs into account. In general audiences, when you play that little game, they say, wait a minute, what did he do? Wait, that can't be right. I mean, forget datas and standard deviations and equilibrium and all that, just that argument from pure arithmetic. And the money managers hate to hear that because they don't want to have to have that discussion with their clients.

It's a paper, I published a two-page paper on the arithmetic of active management. Sharpe's math, I'll link to that in the show notes for our podcast listeners, they can check out that paper by Bill. There have been attempts by many managers writing articles to say, well, but there are new issues.

We get them, the good ones first, and there's this and there's that. Those are minor perturbations, realistically. And that argument for indexing, I mean, it's so self-evident, virtually everybody in the Boglehead group knows it. Let's move on to some questions on model portfolios next. This one is from username Exodusing from the Bogleheads forums who writes, a general principle is that people who are much different from the average investor, as weighted by portfolio size or trading activity, those people should deviate from the market cap weighting to take into account their special differences.

Does Bill agree? And then we had a similar question from username Tom76. Let me break that into two pieces. One is less risk, more risk. And in the theory, you can do that by borrowing and lending. And in the theory, you can borrow and lend at the same rate, but those are very strong assumptions.

There's one market portfolio levered up or down. And of course, people don't just take one market portfolio and lever it up or down. They tend to shade a bias towards less risky funds for a bias towards more risky, et cetera. The real world is more complicated than the simple models that economists create.

People cannot borrow at the same rate at which they can lend or risklessly invest. There are arguments there and I will not argue that life is as simple as in our simple models. And again, you need to take your whole portfolio into account, your assets. If you have a home, an occupied home, that's an asset.

If you have a mortgage, that's a liability, et cetera. I sort of think of that as more a bond stock issue. Now in the simple theory, you know, there's the market portfolio includes bonds and stocks and you lever that up or down at the riskless rate. Well, let's face it, we really don't do that.

I think a lot of those issues can be addressed by changing the proportions of bonds and stocks. And that I think is the lever that I would prefer to see people pulling and pushing to get a balance. And that goes back to that basic Boglet's principle, which is take the right amount of risk.

And you can do that by adjusting that lever. How much do you want in bonds versus stocks? Yeah, that would certainly be the place to start at the very least. I wonder if Exodus is asking about factor investing in this question. Some people's favorite strategy of overweighting small stocks, for example, you can do that with index funds.

I don't advocate overweighting small stocks because you think they're underpriced. More risk for the chance at higher return. Those higher returns are not guaranteed when overweighting small caps. Let's talk about TIPS, Treasury Inflation Protected Securities. These are inflation-adjusted government bonds. We have another question from Boglet's forums. This user writes, "Now that TIPS have positive real yields, should individual investors who have enough space in tax-deferred accounts be using them exclusively instead of regular or nominal treasury bonds?" It's certainly nicer now that they have positive.

It's not so nice for those who help them if they need to sell them. Well, definitely in an important sense, TIPS for somebody in the U.S. are the riskless security or as riskless as you can get in terms of consumption. Let's return to a question that we touched on earlier on factor investing, such as those factors found by Fama and French.

Do you believe in those factors? Well, believe is perhaps too strong a word. Are they useful? Yes, for some things they are. But do I believe that it is clearly true that people should overweight exposure to a small factor or a gross factor or whatever factor of your choice because there's something wrong with the markets?

No. What are your thoughts on international diversification? Should investors be only investing in the U.S. total stock market or should we be investing globally? I'll have to tell a story here. I was on a nonprofit investment committee and one of the members was a semi-retired private equity guy. And we had a consultant who was helping us, et cetera, the usual story.

And at one point we were discussing a foreign investment and he gave a little speech as far as I could tell was not kidding, said, well, if he had his druthers, we wouldn't have any foreign investments because they don't know how to run businesses over there. And I thought, well, surely, okay, haha, this is a joke.

It wasn't. He was serious. That's one view. It's not mine. My view is that international diversification should be a good thing in theory as long as people can without too many problems in terms of repatriation and all the rest and divergent tax systems. I believe in globally diversified portfolios, there is a sense of diversification.

That said, there is an argument for investing at least more than market proportions at home because that's where a lot of your consumption originates. You know, if in fact the company that you have traditionally purchased goods at the grocery store does very well because they raise their prices a lot, you at least have a balance.

Well, I'm paying more, but my stock went up and that's a trivial and sort of a silly example. So I think there is an argument for home bias, but I don't think it's totally offset by the advantages of global diversification. So there's a happy point in the middle somewhere there.

For those who aren't investment nerds, know that the global cap weighting is roughly 60/40. That's to say roughly 60 cents of every dollar invested around the world is invested in U.S. companies and the balance of that 40 cents is invested outside of the U.S. So that is the global cap weighting.

If we have a home bias, we'll invest a little bit more than that roughly 60% compared to international. For example, Rick Ferry, the normal host of this podcast, frequently suggests 2/3, 1/3 in favor of U.S. stock markets, giving us a little bit of a home bias. He talks about that in episode one of the Bogleheads Live podcast.

I'll link to that in the show notes for our podcast listeners to check that out. Bill, what do you think is a reasonable mix for home bias? Whether or not you go to world market proportions, which is what I would favor as a default. Ask yourself, I don't buy only companies in California, I buy companies in the U.S.

and I don't buy only companies in the U.S. I think you need to really think a little bit about what are your other holdings. You obviously have a disproportionate holding in the U.S. if you own your own home. So if you take your overall portfolio, including things like equity in your home, then that gives you a difference.

Certainly if you've got real estate, your primary residence, maybe even some investment properties, then that further tilts you towards that home bias. Then if you've got that global cap weighted portfolio for your liquid investments, that is a phenomenal point. There was a time there was some investor would say, I only invest in things that are close to home.

You think, no, wait a minute, that's from a diversification standpoint, you win a lot of stake in California or if what have you from your property. Let's talk more about bonds. Bill, I'm curious about your thoughts on the following. The risk of equities shows up in corporate bonds, therefore, if I'm trying to manage equity risk, I don't want to hold bonds that are subject to equity risk in my portfolio.

That means opting exclusively for U.S. Government bonds for the bond portion of my portfolio as advocated by David Swenson, the late chief investment officer over at Yields Endowment. I haven't thought of the issue that way. Why should it matter in what manner you invest in the company? It's out there.

It's part of the market, broadly construed. There is obviously the risk issue. If you take the simplest of a theory, in theory, you should deal with combining the overall market with riskless securities to deal with your risk aversion and you should get everything that's out there in the market, if you can get it at reasonable expense.

Now kinds of issues you're raising are more subtle, theory is not subtle enough to deal with it. My first impression would be whatever the company's issued will buy our proportionate share of everything and then leverage to move the overall risk of the portfolio up or potentially down. Barita Lover from the Bogleheads Forums asks, "Is chasing higher yields via a lower-duration bond in the current environment a viable strategy?" Well, I would just say generically anything that assumes that you can exploit somebody who is dumber than you would not be recommended if you believe in efficient markets.

What are your thoughts on changing bond maturity over time, that's to say right now short-term yields are really attractive, therefore I'm going to hold a short-term bond portfolio and then maybe when rates normalize, I'll update my bond portfolio going farther out on that yield curve. What do you think about market timing your bond portfolio with respect to interest rates?

Yeah, in general, I don't think much positively about market timing because market timing means the other people in the market are stupid or at least not as smart as you are. And there are a lot of smart people in the market. It's not at all clear that you know significantly more than is embedded in the market.

Maybe you do. I think you know more about the future than the average investor and you have to think of the average investor as dollar-weighted, not the average investor, you know, down the street with a small portfolio. The average investor is pretty informed and pretty smart. If you're going to underweight or overweight anything because you think the market is quote got it wrong, then you're betting against a bunch of folks, many of whom in terms of dollars invested, know a lot about some of these things.

I do not play that game and I would not recommend it to the average investor. What are your thoughts on foreign bond holdings? This question is from user name McHugh from the Global Heads Forums who asks about just holding the U.S. bond market on the bond portion of their portfolio.

Well there's an argument you should overweigh that which you eat. In other words, you live in the U.S., you buy things from the U.S. predominantly, although not exclusively of course, there would be an argument for doing things that are closer to your consumption basket, put it in economist terms, and I think that's an argument worth thinking about.

Of course, we consume a lot of things that in whole or in part come from elsewhere, but the whole bias, you know, maybe makes some sense, but you have to think about it that way I would argue as you make the decision. Let's talk a bit more about real estate.

This question is from user name Abbas368 from the Bullguards Forums who writes, what are his thoughts on private real estate investing, such as Fundrise and Grant Cardone, as an alternative asset class to invest in alongside a diversified low-cost total market index fund portfolio? I think you should certainly get market proportion, think about market proportions of real estate in the sense of things that are traded on security markets where you've got liquidity, et cetera, not in the underlying asset, but in the security.

When you start talking about direct investment in real estate, that raises a number of other conditions. I mean, you're not going to try to get a piece of every shopping mall. I think it's a practical matter. There are traded securities on major markets, that's definitely something worth considering in proportions on those markets.

Abbas368 goes on to say, these funds typically have high fees, such as 1% and are illiquid. Does that illiquidity increase the probability of achieving alpha? Well, I would not argue that anything with certainty increases the probability of increasing alpha. I think there's a pretty good argument that the truly average investor should consider liquidity.

You obviously don't do it when you buy your own house. You buy real estate that's illiquid because you can live in it, but to buy on the illiquid asset as an investment, period, I think you should give some thought before you do that. Let's talk about publicly traded REITs.

For example, using Vanguard's low-cost REIT index fund, V&Q, these were highly recommended 10 to 20 years ago by Burton Malkiel and David Swensen. I think you should consider investing in them in market proportions, in the risky part of your portfolio. Again, if they're highly liquid and they're traded reputably and such, yes.

When you invest in VTI, VTSAX, that low-cost Vanguard total stock market index fund, you're already getting everything in V&Q, to your point. Let's pivot to annuities. This one is from username Afan from the forums, who writes, "Can you discuss the role of annuities versus bonds in a retirement plan?" Annuities versus bonds, well, there's a really big difference.

When you die, your kids can tell there's a difference, or your universities, and that when you die and holding annuities, there's nothing for anyone else. That's a major difference, and the whole issue of should you annuitize, should you partially annuitize is one that takes an awful lot of thought.

There are very, very important things that transcend investment discussions on whether you should annuitize or not. One of the questions is whether or not you can even make it to a very old age, which you have some probability of reaching. And do you want to play the probabilities, or just say, "I'm not going to bet that I'm going to die soon"?

It's a very complicated decision that involves many issues that transcend or at least overwhelm the economics involved. A single premium immediate annuity, that's the type of annuity you described just now. Let's jump to some questions that you suggested about asking artificial intelligence, AI, how to invest. It's pretty interesting.

First of all, of course, as you well know, everybody now well knows the answers. It's astounding what kind of answers you can get. Answers do differ. I asked the arithmetic of active management, "Can the average dollar invested in a market portfolio after costs outperform the average dollar invested in active strategies?" And one of them said, "No, period." One has to think about what the role of AI will be in investment advice, whether it will replace some humans or it will just give advice to people who otherwise didn't get it, and what the impact of that might be.

We need to find a way to make sure that the AI reads some of the things that you and I are talking about and such. Certainly, at least for the short-term inspirer, be aware if you're using those AI platforms for investment advice. Amen. Bill, thank you so much for your time.

I really appreciate it, as I'm sure as do all the Bogleheads. Any final thoughts you'd like to share with the Bogleheads? My guess is the Bogleheads are on pretty much the right course, if they're truly following Jack. That's a very good thing. I appreciate your interest and I appreciate their interest and I appreciate anybody who listens to whatever the edited version of this will be for spending the time.

And that wraps up our interview with Dr. William Sharpe. Don't forget, you've still got time to take advantage of the special room rate for the hotel for the 2023 Bogleheads conference. Go to boglecenter.net/2023conference for more information. I'll be back next month returning as guest host for the Bogleheads on Investing podcast.

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Thank you for checking out this episode of the Bogleheads on Investing podcast. If you want to submit questions for next month's guest, check out the Bogleheads forums. We have a thread going for questions for Jonathan Clements of the Humble Dollar, who will be our guest on the next show.

I'll link to that thread in the show notes so you can drop your question for Jonathan Clements. Until that next show, have a great one.