All right. Lesson 1.8 aka assignment two. So, remember I said module one is building up the fundamentals so this will be the only module where we have two assignments involved. In this lesson two parts and as we talked about with assignment one, the first part is just actually giving you the questions for assignment two which you're going to give the old college try to first then after giving it your best attempt, see my discussion, see the answer key for assignment two. What's the key point of this assignment? Getting a measure of how important is it to add other assets to your portfolio and in particular looking at from a US investor perspective. Is there much benefit to adding gold if you're already holding US large-cap stocks, if you're invested in the US stock market, is there much benefit to international diversification are the two key points of this assignment and I think give valuable lesson for real-world investment practices. We talked about this before. I think it's worth highlighting again for this assumption. Bill Sharpe here design capital asset, one of the people who wrote about the capital asset pricing model in the '60s. It provides a nice reality check before we get into doing this work and coming up with these portfolios. It's always perilous paraphrasing him to assume that future will be like the past but it's at least instructive to find out what the past is like. So that's the purpose of us doing these analysis. We're taking assumptions, we're basing our assumptions on return distributions that we've measured in the past and seeing what that predicts for our portfolio assuming these return distributions will continue into the future. If you don't like the assumptions for the return distribution, the great thing about the spreadsheet is you can go in and make different changes and see how the portfolio or optimal portfolios change and then talk further about these assumptions that when we're historical data are pretty useful, are quite useful and we're looking at standard deviations reasonably useful for looking at correlations and virtually useless for expected returns. Now one thing just, maybe a little caveat to that, if you're looking at average returns over a very small time period where there's a big bull market or big bear market, of course the average return there is going to be far different and from what we've observed historically. I'm going to be looking at averages and return distributions obtained over wide samples of data. So it still might be the case that the past doesn't really predict what these average returns are like to the future but at least it's not going to be based on like one or two years, it's going to be based on 20, 40 years worth of data. So, this assignment is going to have two parts, two portfolio allocations, six questions total. So when we're looking asset allocation we first start out with small and large, small large value and growth was another example we consider. Now let's expand it up to five assets. So we're maximizing the optimization routine or spreadsheet that I put in. Remember I created rows and columns for five different outlets so we're using all of them and now we're adding gold to the mix here. So it doesn't make sense to add gold to the portfolio. So we're going back 40 years, 40 years worth of monthly data and this data to use for your assignment is contained in the spreadsheet. The name says what it is, Efficient Frontier- LargeSmall-ValueGrowth-Gold. So use a spreadsheet to do the first part of assignment two. We get our data on stock returns, large stocks, small stocks, value stocks, growth stocks. Again from the Ken French Data Library which he generously posted online, large, small or looking at the top 10 percent and bottom 10 percent of firms raised on the size of the market value of their equity value and growth or look at the top 10 percent and bottom 10 percent of firms ranked by their book to market ratio. So the top 10 percent, think of this cement company, high book to market value where there's a lot of tangible assets in place for the growth stocks. Bottom 10 percent of book to market, think of the Internet startup with a great idea that investors are excited about but there aren't actually any tangible assets in place except for maybe a computer server or just an intangible little property or like that. But most assets are intangible in nature for the growth stocks and we add to this now gold price data from which we can calculate the return on golds from the Deutsche Bundesbank Data Repository. So, we have monthly data over 40 years, so I guess that's 480 monthly observations or returns from these five asset classes where you can calculate average returns, standard deviations, correlations across these assets. So let's look at the questions that I'd like you to tackle given the assumptions that I gave you in the spreadsheet. Remember those assumptions are derived from the historical distributions over the 40 year period, 1975 to 2014 for these asset classes. Question one. Suppose that you are currently 100 percent invested in large stocks and you cannot short, so portfolio weights cannot be negative, so your current situation 100 percent in large stocks. You like the risk of large stocks so you may change your portfolio but you don't want to change your standard deviation of the portfolio, what portfolio maximizes expected return subject to having the same risk level of large stocks? What's the expected return in this case, and what are the portfolio weights? What is the new portfolio and then how much are returns expected to increase if you switch from large stocks to this new portfolio? Another way of saying this is how dominated is large stocks in this Efficient Frontier? Question two. Suppose you can short assets now, so it's just like question one only question one difference. Let's highlight that here. Now, you can short assets, so the exact same question we had before, but now you can short assets. You like the risk of large stocks. So, what is the optimal portfolio given you can short where you maintain the same risk as large stocks. What's that portfolio allocation? When you put a portfolio together, which asset do you short? When you're allowed to short and come up with a portfolio that gives the highest return subject to having the same risk as the large-cap fund, what asset do you short in this portfolio? What asset has the biggest increase in portfolio weight when you go from this scenario of you cannot short? When you go to this scenario you can short? That's a second part of the question here, which says the biggest increase in portfolio weight, when you go from CANNOT short to CAN short examples. So, what's the benefit at the end of the day when you go from question one to question two, what's the benefit in terms of higher expected returns? By being allowed to short and then given this benefit in higher expected returns, is it worth allowing the investor to short. So, do you have a big increase in expected return of the portfolio by being allowed to short or is there a small increase when you're allowed to short, what asset do you short? What asset increases a lot positively in terms of portfolio weight? Why is that the case? Question three, let's go back to suppose you CANNOT short, what's the expected return portfolio standard deviation and portfolio composition of the portfolio that maximizes the Sharpe Ratio? Excess return of the portfolio divided by the portfolio standard deviation. Does GOLD have any part in this portfolio? If it does, why is gold apart of the maximum-Sharpe Ratio portfolio? If GOLD is nowhere to be seen, its portfolio weight is zero, given you can't short. Why is Gold not a part of it? So, that's the first half of the assignment, the first three of the six questions. The second part is the great thing about this course is students from around the world. So, let's consider, is there a benefit to international diversification? When it comes to traveling and meeting folks the answer's definitely yes, but how about in terms of financial investments here. So, asset allocation with international stocks, here we're going to refer to this spreadsheet EfficientFrontier-US-International. That spreadsheet you're going to use for the second part of assignment two, that has the average return, standard deviations, correlations between US index fund, Japan valuated stock market, Asia Pacific excluding Japan and Europe. This data's available on the Kenneth R. French Data Library starting July 1990, so the weird starting date is just because that's the first month we had the data through 2014, so well this almost 24-25 years worth of data that we have here, monthly data to do the correlations in stock returns, calculate standard deviations, averages across these three regions of the world. All right. So, question four on the assignment, this is a first question regarding international exposure but question four on assignment two. So, it's well known that there's a home bias in investing, people tend to invest in stocks and assets in the country where they're from. So let's say, we're from the US and we have 100 percent in the US stock market and we like comfortable with the risk of investing in US stocks, but we're open to an alternative portfolio as long as a portfolio standard deviation is the same as US stocks. So, this is asking, given a portfolio standard deviation is the same as US stocks, what portfolio can we put together with international exposure that gives us the highest possible return? So maximize the return given the risk of the US stock portfolio. What are the components of that portfolio? What is the return? We know the standard deviation is the same as the US stocks and then the key question is, does this portfolio offer us much higher return than the scenario where we're 100 percent in US stocks? Question five, again suppose you cannot short. What's expected return and standard deviation of the portfolio that maximizes the Sharpe Ratio? What are the portfolio weights? Does Japan have any part in this portfolio that maximizes the Sharpe Ratio? If yes, why is Japan part of the portfolio? If no, why is Japan not? So, what's a portfolio that gives us the biggest bang for the buck, the biggest Sharpe Ratio, does Japan have any part in it? Question six, again suppose you CANNOT short, Japan has not performed well over the last 25 years, so when you look at their assumptions for returns they're very low. What if we change that assumption so Japan has the same projected expected returns as Asia Pacific? So, we bump that monthly return for Japan up to 0.96 percent per month, the same as Asia Pacific. What's the maximum Sharpe Ratio now with this change assumption? What is the portfolio that gives us this maximum Sharpe Ratio, expected return, and the standard deviation? Hey, let's talk a bit about the initial portfolio weights in Excel Solver, I know this is a topic you can't wait to get into. The two Excel spreadsheets to use for assignment 2 and less than 18 are; Efficient Frontier, large, small, value, growth, goal and EfficientFrontier-US-International. When you open them up, you will notice that both of these spreadsheets start out with mixed portfolios. They are not starting out with 100 percent invested in one asset, like a 100 percent in US stocks, indeed both initial portfolios have the portfolio weights equally split across the assets. There is a reason for this, sometimes an optimization algorithm, like that used by Excel Solver, can have a hard time finding an optimal solution that is a constrained maximum or minimum. If the search starts at a corner, that is, a portfolio allocation is 100 percent in one asset. Thus, please start out using my initial portfolio weights already in the spreadsheet when using Solver to answer the problems in assignment two. So, as we talked about with assignment one, it's always good to be curious but not so much in this case, what's our rule? Do the assignment first, give it the college try. After you do the assignment, you're free to go in, look at my discussion of the assignment, if you want to change your answers after seeing my discussion, that's fine but try it on your own first, right? It's in your own interests to see, to give you knowledge of the material, then reviewing the answers is fine. Before you grade or review other people's work, please look at my discussion so you get a better sense of what answers to look for and what the correct responses are. Hopefully, your first attempt and my answers are perfectly correlated with each other.
