Tag Archives: diversification

MPT and retirement planning

In a previous post, I questioned how diversified a portfolio of just three assets could really be.  This wasn’t really fair, since the whole point was to avoid such an analysis.  To provide a fairer test, I will use 15 assets for this analysis, all of which are choices taken from an actual retirement plan. The 15 securities listed here consist of 14 mutual funds and a stock.  Choices are predominately focused on US equities, though is a REIT fund (FARCX), two international funds (RERGX, VTRIX), a bond fund (PPTRX), and a money market account.  Given this expanded universe of choices, what will theory tell us is best?

I used Matlab and it’s financial toolbox to retrieve four years of monthly prices for each of the funds.  Since one of the funds is a target date fund, data was not available for it before then.  The data was provided free of charge by Yahoo Finance.  These prices where used to calculate monthly returns, which were in turn used to get means and covariance of the assets.  Once this was done, Matlab’s financial toolbox was used to find the optimal weights.  If you really want to get in to the details of such a calculation, this book explains it well, but be warned:  linear algebra and calculus is required, so in practice, this problem is best left for software.  Below is a screen capture of the results, as well as a graph of the efficient frontier.

 efrontierweightsAndNames

The results of the analysis show that fewer assets are better, but raise a few questions as well.  Efficient portfolios generally consist of 3 assets.  This seems to support the idea that a few assets will do.  Yet while these portfolios are efficient with respect the risk reward trade off, they take no account for where the return comes from.  In this case, the funds are for the most part positively correlated over the time period, so funds that would provide diversification are ignored for the higher yielding choices. This points to the period being too short, or more importantly, the number of choices is too small.  The needed number of assets to consider may be close to 100! This seems to indicate that for retirement planning, MPT may be a nice theory, but it’s real value is as a lesson about the value of diversification.

But what’s this say for our choices? There is no substitute for true diversification.  Getting exposure to assets that are uncorrelated is key.  Considering the 15-asset universe, almost every portfolio on the efficient frontier consisted of 3 assets, but a truly diversified portfolio consisting of the choices offered may be better off with a couple more funds.  In this case, examining the top holdings of the funds would provide as much insight as this analysis did!

In search of diversification

In this past weekends Wall Street Journal, I came across an article entitled Funds Investing:  Make More Money and worry less.   At first glance this article seemed to be stating the obvious.  However, after reading it, I began to wonder.  Can one really get diversification from as little as 3 assets?  After some rough analysis, it seems people may need to worry a little bit more then the article suggests.

The article is actually a summary of ways “lazy” people save for retirement.  Lazy, here does not indicate sloth, but rather to retirement ideas named “the margarita”, “the coffeehouse” and “the no brainer”.  The idea of these “lazy” portfolios is that they don’t require a lot of attention or financial know how to set up.  Given the state of most people’s retirements, lets compare the ideas of these retirement plans, requiring little more then your contributions, to conventional wisdom about what it takes to have a solid retirement.

But suppose we have some time, as well as a computer with Matlab or Excel installed on it.  The question I want to ask is:  given these small quantity of assets that make up these lazy portfolios, what do other philosophies about portfolio management say about theses savings ideas?

What follows is based Modern Portfolio Theory, as told in Burton Makail’s “A Random Walk down Wall Street”.   The mathematical analysis, carried out in Matlab, can be done by hand using a general optimization technique called the method of Lagrangian Multipliers.

Modern Portfolio Theory says that the best portfolios lie along the efficient frontier.  This is a line representing the portfolios that invest all the available funds lie on a hyperbola.  The top half of this hyperbola represents what is called the efficient frontier.  These are the portfolios that invest all money, and receive a higher return then the one that lies on the bottom half.  The portfolio located at the “point” is called the Minimum variance portfolio.  The efficient frontier for a portfolio consisting of the 3 mutual funds is shown below.

effcientfrontier

Taken from Matlab 2012

So consider the portfolio mentioned specifically in the article.  It is a portfolio of 3 vanguard funds, (40% VTSMX (Total Stock Market), 40% VGTSX (Intl. Stock Index), and 20% VBMFX, a bond fund). Using Matlab to calculate things like mean, variance, and covariance of the three assets, using data from Morningstar, we can optimize the weighting of the assets to get the optimal combination.  The weights of the portfolios that lie on the efficient frontier are listed below.

Capturedaweights

Using the Vanguard funds listed in the article, as well as data on historical returns from Morningstar, I computed the efficient frontier for the 3 assets given in the article.  This analysis shows that while the portfolio may provide exposure “…to every major equity offering in the world”, it is not exactly efficient.  The second asset (the international stock fund) seems to have very little place in this portfolio despite the unique exposure it brings.  Clearly blindly quantitatively optimizing your portfolio may not leave you diversified, but being lazy may not get you there either.

(Revised) Owning Bonds Despite a Bearish Perspective

During the financial crisis, the Federal Reserve (Fed) cut the federal funds rate from above 5% to below 1% and has not raised rates since.

fredgraph_effectivefedfunds

As seen above, the grey shaded area represents the recent financial crisis. After reaching the zero lower bound (ZLB) in late 2008, the federal funds rate target has remained at 0.00-0.25%. With interest rates unable to go any lower due to the ZLB, the only way interest rates can move is upwards. The only question is – when will the Fed decide to raise rates?

Although I have been bearish on bond prices for some time, I have not traded on this perspective because I did not know when rates would rise. I am bearish on bond prices because bond yields and bond prices have an inverse relationship (ex. when interest rates rise, bond prices fall). As the economy improves, the moment that interest rates rise (and bond prices subsequently fall) approaches. Following the march FOMC meeting, I have come to believe that rates will rise in 2015. According to the Wall Street Journal, “If you expect lower returns from an asset class than it has provided historically, such as lower returns from bonds, then the math, and probably logic, would tell you to lighten up on bonds”. In order to lighten up on bonds, I would need to sell any bonds that I own. However, I do not own any bonds so I have considered shorting bonds instead through an exchange-traded fund (ETF) such as ProShares UltraShort Lehman 20+ Year Treasury.

Although this investment logic might be right, I have made a mistake by not having any exposure to bonds in the first place. According to the Wall Street Journal, “To be clear, the solution is not to eliminate bonds from your portfolio because they will still provide the very important diversifying benefit of cushioning your portfolio if the market should pull back”. Diversification is an important part of asset allocation that helps reduce the variance of expected returns through decreasing (and potentially eliminating) unsystematic risk from one’s portfolio. In a well-diversified portfolio, only systematic risk remains. On the one hand, systematic risk is correlated among all securities (i.e. macroeconomic news). On the other hand, unsystematic risk is uncorrelated among all securities (i.e. industry or company specific news). Traditionally, stock prices and bond prices have demonstrated a negative correlation. Adding bonds to my portfolio, which consists entirely of large cap U.S. equities, would offer me meaningful benefits through diversification. Recently, irregularities in the relationship between stock prices and bond prices (i.e. a positive correlation) due to quantitative easing might lead one to think that the benefits of diversification are lessened or eliminated. According to Burton Malkiel, “But note that even though correlations between markets have risen, they are still far from perfectly correlated, and broad diversification will still tend to reduce the volatility of a portfolio” (212). Although Malkiel was not referring to quantitative easing, he makes a useful point. As long as two securities are less than perfectly correlated (i.e. less than 1), then there will be benefits from diversification. With my portfolio consisting entirely of large cap U.S. equities, I could reduce the variance of my portfolio’s expected returns through diversification.

Despite my bearish view on bond prices, there are still ways for me to purchase bonds and gain the benefits of diversification. My bearish view on bonds is due to interest-rate risk. In this case, increasing interest rates will push down bond prices. If I wanted to still purchase bonds in order to diversify, then I could purchase bonds with short maturities. The shorter the maturity of a bond, the less it is subject to interest rate risk. This can be seen in the yield curve, which has a positive slope as maturities increase (and the credit rating remains fixed). Although the prices of short term bonds will still fall as rates rise, there will still be benefits from diversification.

As I attempt to adjust my portfolio’s asset allocation, I will consider both diversification and my bearish perspective on bonds. On the one hand, I will purchase bonds with short maturities. On the other hand, I will sell (i.e. sell short) bonds with long maturities. As a small investor, I will use ETFs in order to implement my strategy because it is more cost effective.

Owning Bonds Despite A Bearish Perspective

I enjoy following financial markets and implementing investment ideas in which I am confident will perform as expected. Recently, I have become bearish on bond prices. I am bearish on bond prices because interest rates are low and are expected to begin rising in mid-2015. Bond yields will rise as interest rates rise, which also means bond prices fall (i.e. bond yields and prices have an inverse relationship). As a result, I am thinking of ways that I can trade on this perspective. According to the Wall Street Journal, “If you expect lower returns from an asset class than it has provided historically, such as lower returns from bonds, then the math, and probably logic, would tell you to lighten up on bonds”. In order to lighten up on bonds, I would need to sell any bonds that I own. However, I do not own any bonds so I have considered shorting bonds instead through an exchange-traded fund (ETF) such as ProShares UltraShort Lehman 20+ Year Treasury.

Although this investment logic might be right, I have made a mistake by not having any exposure to bonds in the first place. According to the Wall Street Journal, “To be clear, the solution is not to eliminate bonds from your portfolio because they will still provide the very important diversifying benefit of cushioning your portfolio if the market should pull back”. Diversification is an important part of asset allocation to protect against the random walk of financial markets. For example, eliminating my exposure to bonds and only being exposed to stocks puts me at extreme risk of loss if the stock market declines. According to Burton Malkiel, “But note that even though correlations between markets have risen, they are still far from perfectly correlated, and broad diversification will still tend to reduce the volatility of a portfolio” (212). With my portfolio consisting of 100% large cap United States equities, I am subject to a significant amount of volatility. By adding some exposure to bonds, I might be able to reduce the volatility of my portfolio.

Despite my bearish view on bond prices, there are still ways for me to invest in bonds and gain benefits from diversification. My bearish view on bonds is due to interest-rate risk. In this case, increasing interest rates will push down bond prices. If I wanted to still purchase bonds in order to gain some exposure, then I could purchase bonds with short maturities. The shorter the maturity of a bond, the less it is subject to interest rate risk. This can be seen in the yield curve, which has a positive slope as maturities increase. Although the prices short term bonds will still fall as rates rise, there will still be benefits from diversification.

In addition to interest-rate risk, bonds are also subject to default risk that arises when a debtor fails to pay back the creditor. If a debtor is thought to have a high risk of default, then that debtor is charged a default risk premium and charged a higher rate of interest. If I wanted to still purchase bonds in order to gain some exposure, then I could purchase bonds with a higher risk of default. This is another way to still own bonds and decrease interest rate risk. In addition,  there will be benefits from diversification.

The Best Time to Start Investing For Retirement Is Now

While it may be a long ways away for the students in the monetary and financial policy class, financial wisdom states that now is the time for us to start saving for retirement. As many of us approach graduation and graduate school or our first full-time jobs, we’ll be soon required to answer questions like: “Roth or traditional?” or “mutual funds or ETFs” when setting up our mandatory retirement accounts. Common sense financial knowledge suggests that one should redistribute one’s investment account from stocks to bonds as one ages. This is often formalized in the investing heuristic where one should subtract their age from 100 to determine the proper allocation of stock in their portfolio. However, many financial researchers have had a change of heart and have begun to take a much greater liking to investing in stocks leading up to and during retirement.

Kelly Greene from the Wall Street Journal explains in her article, titled “How Much Stock Should You Own in Retirement?,” that investment researchers have concluded that individuals should invest in stocks in a “U-shaped” pattern in which they invest more heavily in stocks until they near retirement, upon which they dial back their stock holdings to between 20% and 50% of their portfolio at the start of retirement, and then begin to increase their stock holdings by around one percentage point per year throughout retirement. After examining 10,000 simulations with assumed average annual returns of 6.5% for stocks and 2.4% for bonds, the authors explain that those that instead keep 60% of their portfolio in stocks throughout retirement are likely to run out of money after 28 years in the worst case scenario. According to Professor Wade Pfau, a retirement-income professor at American College who was one of the researchers involved,

“You want to have the lowest stock allocation when your portfolio is largest, and that’s going to be right before and after retirement. That’s when you’re most vulnerable to losing wealth. Once you transition into retirement, you no longer have as much ability to change your plans and make it back up.”

This makes sense given the fact that many baby boomers are expected to live into their 80s, meaning that if they retire at the traditional age of 65 they may require a retirement account that could last them upwards of 15-20 years. In this case, retirees can reduce their risk at the beginning of retirement when they are most risk averse, and slowly dial up their risk as they age, thus increasing the odds that they’ll have enough money throughout their life.

It seems that stocks should remain a critical part of ones portfolio even after retirement, so what portion of one’s portfolio should one keep in stocks when one is far from retirement? In his article “Why My Retirement Savings Accounts are Currently 100% in the Stock Market,” Professor Kimball explained that 100% of his paper assets are currently diversified stock market index funds. If we look at this decision using knowledge gained from Burton Malkiel’s “A Random Walk Down Wall Street,” this appears to be a strategy that returns relatively high rewards for low risk. Why? First, there is the decrease in risk that comes with investing in a diverse index fund. By splitting up the investment among dozens of different companies, one can reduce the probability of losing a substantial amount of money in the presence of a random occurrence such as a hurricane or a not-so-random occurrence such as bankruptcy. According to Malkiel, a portfolio of around 60 well-diversified securities (meaning their returns are largely independent) will eliminate nearly all of the unsystematic risk (risk that your portfolio will be in jeopardy after a calamity hits one stock). The systematic risk, or risk that may occur as a result of stock market shocks, can be further diversified away by investing in many different markets, such as by investing in U.S. and European stocks. Kimball’s investment in the Fidelity Spartan International Fund allows him to reduce the risk that a collapse in one stock market or one economy will negatively impact his annual returns. Beyond risk, it’s also important to consider the rate of return of the fund when choosing where to place one’s savings. In his book, Malkiel cites the research of Jeremy Segal, the author of the investment book “Stocks for the Long Run.” Segal calculated the returns of a variety of assets from 1800 to 2010. He concluded that if one invested $1 in the stock market in 1800, after compound interest that $1 would have grown to over $10,800,000 in 2010. If one had invested that same dollar in bonds, which was the next largest gainer, it would have only grown to $27,604. This demonstrates that out of all basic investment instruments at the disposal of the average investor stocks bring the highest returns. So by investing in a well-diversified international stock fund, such as the Fidelity Spartan International Fund, an investor may expect much higher returns with a relatively low level of risk.