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Weight Your Holdings Carefully!

There are different approaches to determining what kind of weight to assign to a particular stock in an investment portfolio. These approaches are best suited for algorithmic trading, since none of these methods will take all of an individual investor’s preferences into account. Nonetheless, different weighting strategies can serve as starting points the investor can use to build a portfolio in the future. One of the simplest strategies is to assign equal weights to the stocks in a portfolio. The assumption behind this strategy is that the investor does not prefer any of the stocks in the portfolio over others. Another simple strategy that is used for the majority of indices is assigning weights proportionally to market capitalization. In this strategy, the investor gives preference to bigger companies. Another popular strategy is assigning weights in accordance with an approach developed by the Nobel Prize winning economist Harry Markowitz. The core idea of this approach is that if we know expected returns and covariance of the securities than we can compose an optimal portfolio. In real word nobody knows expected returns. So usually historical returns are used as proxies for expected returns. But we can also use implied returns (calculated as Price Target/Price) which we’ve discussed in one of our previous articles. At first glance this has much more sense, because implied returns reflect expectations of analysts about future returns of a stock whereas historical returns imply the assumption that future performance of a stock would be the same as its past performance. Let’s test these four strategies for assigning weights to stocks in a portfolio: Equal weights Weights according to market cap Markowitz historical return weights Markowitz implied return weights. Let’s test the different strategies for assigning weights with the help of the Monte Carlo method. We will conduct 100,000 tests, in which we will select a random 20 securities for a random date from 01/01/2008 to 02/01/2015. The conditions for these securities are as follows: The security has to be traded for at least 1 year prior to the date on which the portfolio is put together. The security must have a Price Target on the date the portfolio is put together. We are going to use the strategies specified above for each of these portfolios. Weight limits. In order to obtain results that aren’t heavily dependent on the profitability of one security, we set a 10% limit on the weight of a security. That is, if the market cap strategy assigns a value greater than 10% to a security, the weight will be cut down to 10%. The weights for securities with weights of less than 10% will be proportionally increased. For both Markowitz weighting weight of one stock is also limited to 10% and short selling is forbidden. Let’s calculate the profitability of a portfolio for 1 year. This way, we will get four annual return values for each of the 100,000 random portfolios – one for each weight strategy. The table below gives a summary of the results for this test. The table illustrates how many times each strategy yielded a portfolio with the highest returns, second highest returns, third highest returns and lowest returns. An analysis of the table allows us to make the following conclusions regarding different weight strategies. The Markowitz historical return weights strategy yields the highest return in approximately 32% of cases, and the lowest return in 30% of cases. The strategy results in second highest returns 18% of the time, and third highest returns 18% of the time. These results show that there is a lot of randomness in this method, since the outcomes are concentrated in the lowest and highest ends of the spectrum. These results give credence to a popular phrase – “past performance does not guarantee future results.” The Markowitz implied return weights strategy is more likely to yield the highest returns (37%). At the same time, the worst result also has a high probability (26%). However, the probability of getting the worst outcome is significantly lower than getting the best outcome and doesn’t differ much from the probability of getting the second highest or third highest returns. We are able to achieve this favorable result because implied return is much closer to an expected return, which is necessary for implementing the Markowitz approach. The equal weights strategy yields outcomes that are concentrated in the middle of the spectrum, in the second and third highest return categories. The cap-weighted strategy yields the worst results. This strategy rarely yields the highest returns, and frequently results in the lowest returns. This can be partially explained by the fact that using market cap values to assign weights tilts the portfolio in favor of companies that posted stock price increases in the recent past. That is, value opportunities are deliberately avoided. Thus, the best strategies seem to be the implied return method and the equal weights method. The implied return strategy has a high probability of maximum profits compared to other strategies, but entails more risk. The equal weights strategy is more conservative – it rarely yields the best results, but is also unlikely to yield the worst outcomes. For clarity, let’s look at how these weight strategies work for a portfolio of 20 largest companies from the S&P 500 index from 01/01/2008 to 02/01/2015. The requirements for securities are the same as in the previous test. The table shows the composition of the portfolio at every rebalancing date. 01/02/2008 01/02/2009 01/04/2010 01/03/2011 01/03/2012 01/02/2013 01/02/2014 01/02/2015 Exxon Mobil (NYSE: XOM ) Exxon Mobil Exxon Mobil Exxon Mobil Exxon Mobil Apple (NASDAQ: AAPL ) Apple Apple General Electric (NYSE: GE ) Wal-Mart Stores (NYSE: WMT ) Microsoft (NASDAQ: MSFT ) Apple Apple Exxon Mobil Exxon Mobil Exxon Mobil Microsoft Procter & Gamble (NYSE: PG ) Wal-Mart Stores Microsoft Microsoft Alphabet (NASDAQ: GOOGL ) Alphabet Microsoft AT&T (NYSE: T ) Microsoft Alphabet Berkshire Hathaway (NYSE: BRK.B ) Chevron (NYSE: CVX ) Microsoft Microsoft Berkshire Hathaway Procter & Gamble General Electric Apple General Electric IBM (NYSE: IBM ) Wal-Mart Stores Berkshire Hathaway Alphabet Alphabet (GOOGL, GOOG ) AT&T Procter & Gamble Wal-Mart Stores Alphabet Berkshire Hathaway General Electric Johnson & Johnson (NYSE: JNJ ) Chevron Johnson & Johnson Johnson & Johnson Alphabet Wal-Mart Stores General Electric Johnson & Johnson Wells Fargo (NYSE: WFC ) Johnson & Johnson Chevron JPMorgan Chase (NYSE: JPM ) Chevron General Electric IBM Wal-Mart Stores Wal-Mart Stores Wal-Mart Stores Pfizer (NYSE: PFE ) IBM IBM Berkshire Hathaway Chevron Chevron General Electric Bank of America (NYSE: BAC ) IBM AT&T Procter & Gamble Procter & Gamble AT&T Wells Fargo Procter & Gamble Apple JPMorgan Chase General Electric AT&T AT&T Johnson & Johnson Procter & Gamble JPMorgan Chase Cisco Systems (NASDAQ: CSCO ) Wells Fargo Chevron Johnson & Johnson Johnson & Johnson Pfizer JPMorgan Chase Facebook (NASDAQ: FB ) Altria Group (NYSE: MO ) Coca-Cola (NYSE: KO ) Bank of America JPMorgan Chase Pfizer Procter & Gamble IBM Chevron Pfizer Alphabet Pfizer Wells Fargo Coca-Cola Wells Fargo Pfizer Pfizer Intel (NASDAQ: INTC ) Cisco Systems Cisco Systems Oracle (NYSE: ORCL ) Wells Fargo JPMorgan Chase AT&T Verizon Communications (NYSE: VZ ) IBM Verizon Communications Wells Fargo Coca-Cola Philip Morris International (NYSE: PM ) Coca-Cola Amazon.com (NASDAQ: AMZN ) Oracle Citigroup (NYSE: C ) Oracle Coca-Cola Bank of America JPMorgan Chase Oracle Coca-Cola Bank of America AIG (NYSE: AIG ) Intel Oracle Citigroup Oracle Philip Morris International Bank of America Coca-Cola JPMorgan Chase HP Inc. (NYSE: HPQ ) HP Inc. Pfizer Intel Bank of America Oracle Intel Coca-Cola PepsiCo (NYSE: PEP ) Intel Intel Merck & Co (NYSE: MRK ) Verizon Communications Citigroup AT&T The table below contains the results of the test. Because the overall number of tests is a lot lower compared to the table above, the results are also different. However, there are some similarities. The Markowitz implied return weights strategy produces the best results more often than other strategies, but also yields the lowest profitability more frequently than other strategies as well (same as the Markowitz historical return weights strategy). This is consistent with the previous findings, which suggest that this strategy produces outcomes that are concentrated on opposite ends of the spectrum, with a higher probability of the best outcome. The Markowitz historical return weights strategy also yielded results on opposite ends of the spectrum, but the probability of getting the worst possible outcome was higher (this is also in line with the previously obtained results). The significant difference between this test and the previous one is that the cap-weighted strategy produced more stable results than the equal weights strategy. However, as in the previous test, both of these strategies rarely yield the best outcomes. Conclusion As noted above, the standardized approach to selecting weights for instruments in a portfolio is unlikely to be the best solution for an investor, with the exception of algorithmic trading. However, the standardized selection of weights can be a starting point for determining how much to allocate resources between different instruments. The test we ran illustrates that out of the following strategies: Equal weights Weights according to market cap Markowitz historical return weights Markowitz implied return weights. The Markowitz implied return weights is optimal for investors who can withstand a lot of volatility, while the equal weights strategy is best for more conservative investors.

3 Best-Ranked Mid-Cap Value Mutual Funds

Mid-cap value mutual funds provide excellent opportunities for investors looking for returns with lesser risk by gaining exposure to stocks that are available at a discounted price. While large companies are normally known for stability and the smaller ones for growth, mid caps offer the best of both the worlds, allowing growth and stability simultaneously. Companies with market capitalization between $2 billion and $10 billion are generally considered mid-cap firms. Meanwhile, value mutual funds are those that invest in stocks trading at discounts to book value, plus having low price-to-earnings ratio and high dividend yields. Value investing is always a very popular strategy, and for a good reason. After all, who doesn’t want to find stocks that have low P/Es, a solid outlook, and decent dividends? However, not all value funds solely comprise companies that primarily use their earnings to pay dividends. Investors interested in choosing value funds for yield, should be sure to check the mutual fund yield. Below, we share with you 3 top-rated mid-cap value mutual funds. Each has earned a Zacks Mutual Fund Rank #1 (Strong Buy) and is expected to outperform its peers in the future. Lord Abbett Mid Cap Stock Fund A (MUTF: LAVLX ) seeks capital growth. LAVLX invests heavily in securities of undervalued companies having medium size market capitalization. LAVLX invests in companies located throughout the globe. LAVLX may also invest in ADRs. The Lord Abbett Mid Cap Stock A fund has a three-year annualized return of 8.3%. As of September 2015, LAVLX held 79 issues, with 2.58% of its assets invested in Hartford Financial Services Group Inc. (NYSE: HIG ). Sterling Capital Mid Value Fund A (MUTF: OVEAX ) invests the lion’s share of its assets in equity securities of undervalued mid-cap companies. According to the advisors, a mid-cap company is defined as one with market capitalization within $1 billion to $30 billion. OVEAX predominantly invests in common stocks of both domestic and foreign firms that are traded in the U.S. The Sterling Capital Mid Value A fund has a three-year annualized return of 10.2%. OVEAX has an expense ratio of 1.19% as compared to the category average of 1.21%. Federated Absolute Return Fund A (MUTF: FMAAX ) seeks positive return consistent with low level of correlation with the U.S. equity market. FMAAX invests in both equity and debt securities of both U.S. and non-U.S. issuers. FMAAX focuses on acquiring securities that are believed to be mispriced or misperceived. The Federated Absolute Return A fund has a three-year annualized return of 3.5%. Dana L. Meissner is the fund manager of FMAAX since 2009. Original Post

Portfolio Analysis In R: Part VI | Risk-Contribution Analysis

Do you know where the risk in your portfolio is coming from? Well, of course, you do. After all, you designed the portfolio, and so the asset weights reflect the risk contribution. A 50% weighting in stocks translates into a 50% contribution to risk for the portfolio overall, right? That’s a reasonable first approximation, but it’s a crude estimate, and one that’s prone to error as market conditions change – particularly for a strategy that holds a mix of asset classes. For a precise profile of the relative contributions from each piece of the portfolio – an essential piece of intelligence for risk management – we’ll have to go deeper into the analytical toolkit. The reasoning for decomposing portfolio risk into its constituent parts is straightforward – the relationship of risk across assets is in constant flux through time. As a result, correlation and volatility are changing. The main takeaway: Your portfolio’s risk profile may differ from your assumptions, perhaps radically so at times. The only way to know if your estimates match reality is to routinely run the numbers and make periodic adjustments to the asset allocation when appropriate. An exaggerated example tells us why this facet or risk management is essential. Let’s say that you’ve designed a portfolio with a 10% allocation to emerging market stocks on the assumption that 10% of total portfolio risk will be driven by these assets. Because of shifting relationships with other assets, however, it turns out that the risk contribution from emerging markets rises to twice your assumption after three months – 20%. The problem is that this change might not be obvious without formally modeling the risk-contribution factor. Let’s dig into some details with a real-world example. As in previous installments in this series (see list of articles below), we’ll use our standard sample portfolio (unrebalanced in this case), which consists of 11 funds for testing a global mix of assets, spanning US and foreign stocks, bonds, REITs and commodities, based on the following target allocations: Calculating risk contribution requires building a covariance matrix and running matrix algebra calculations, but don’t worry – we can streamline the task with user-friendly functions in the PortfolioAnalytics package via calculations in ” R ” (here’s the code for generating the raw data that’s discussed below). For simplicity, we’ll use the conventional definition of risk-standard deviation, aka return volatility. In practice, we can apply other risk measures, such as value at risk, extreme tail loss, and other quantitative metrics. But in the example below, we’ll stick to standard deviation to illustrate the basic outline. As a preliminary step, here’s the risk contribution for the sample portfolio (defined above). Note that this is based on the daily data from 2004 through yesterday (January 11). It’s no surprise to find that the contributions generally align with the target allocations. For instance, the 30% weight for the US stocks (NYSEARCA: SPY ) compares with a risk contribution of roughly 33%, as shown in the chart below. But there are some deviations as well. Consider how real estate investment trusts (REITs) compare in terms of the target allocation versus the risk contribution. We initially allocated 5% to REITs (MUTF: VGSIX ), but it turns out that the risk contribution is twice as high at nearly 10%. Note too that the risk contribution is slightly negative for the allocation to Treasuries (NYSEARCA: IEF ). The negative number indicates the relatively strong degree of volatility reduction that this asset brings to the mix. As a result, the negative risk contribution means that increasing (lowering) the weight to IEF will lower (raise) the portfolio’s volatility. In other words, IEF’s unique role as a diversification agent is quite clear when we run the numbers for this portfolio. The problem with looking at risk contribution across long periods of time as a single data set is that the analysis suggests that this facet of the portfolio is static. In fact, risk contribution is constantly changing. The evolution is usually gradual, but it’s valuable to keep an eye on the changes through time in order to minimize the surprise factor vis-à-vis sudden shifts in the portfolio’s risk profile that may conflict with the investment goals, risk tolerance, etc. For a more realistic (dynamic) measure of risk contribution, we can monitor the ebb and flow based on rolling historical windows. For example, here’ how the risk contributions for the funds compare on a rolling one-year basis, as shown in the next chart below. Based on this history, we can see that the risk contributions are relatively well behaved through time. The allocation to US equities, for instance, has generated risk contributions ranging from the high-20% level up to around 40%. We may or may not find these results satisfactory, depending on the portfolio’s goals and our risk expectations. The key point here, however, is that we now have hard data on the historical relationship between the relative share of risk for each asset. What can we do with this information? There are several applications that may be productive. Let’s consider just one by focusing on the US equity holding (SPY) in terms of its rolling 1-year return versus its risk contribution (see chart below). As you see, there’s a moderately negative correlation between the two metrics. The relationship implies that there may be useful signals here that tell us that an asset allocation adjustment is timely, particularly when the risk contribution and trailing return move to relatively extreme levels simultaneously. Monitoring risk contribution doesn’t replace other risk-management tools – instead, it’s a compliment that enhances our overall risk-management process. It’s part of what is known as the risk budgeting process. Although conventional asset allocation focuses on the relative share of each holding’s capital contribution, there’s a strong case for monitoring portfolios through a risk lens as well. In fact, it’s reasonable to consider the possibilities via a risk allocation process versus a traditional capital allocation framework. Ultimately, it’s the risk exposures that matter for engineering return outcomes. That’s an intuitive point, of course, and one that’s been widely embraced. Using a risk-attribution toolkit allows us to refine the concept in order to maximize the associated benefits and minimize any unexpected results that can arise when relying on vague rules of thumb for managing risk. *** Previous articles in this series: Portfolio Analysis in R: Part I | A 60/40 US Stock/Bond Portfolio Portfolio Analysis in R: Part II | Analyzing A 60/40 Strategy Portfolio Analysis in R: Part III | Adding A Global Strategy Portfolio Analysis in R: Part IV | Enhancing A Global Strategy Portfolio Analysis in R: Part V | Risk Analysis Via Factors Tail-Risk Analysis In R: Part I