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Apply Kelly Formula To Investing: Is Volatility Just Risk?

Summary Kelly Formula is one of the most important formulas in the investment theories. It is also very interesting and useful since it is against our intuition. Volatility is commonly seen as just “risks”, but it is much more than that, since volatility can affect performance too. Theoretically, Kelly Bet is also the “optimal bet”, but that is often not true in practice. Since reducing volatility can help performance too, I will also talk about many methods to reduce the volatility of a portfolio. Kelly Formula Kelly formula or Kelly bet was found by John Kelly in 1956. This formula gives the optimal bet, given fixed odds in a gambling game. Although it has some fairly simple math behind, it didn’t get much attention from the financial world until much later. On the surface, its application is limited. Financial activities such as investments don’t always have fixed odds, and may not have a fixed period for its return either. However, what is profound in that formula is that it gives a “maximum bet” that is optimal even if one is completely non-risk-averse. If we really think about it, it is actually against regular people’s intuition. Normally we would think the returns are always related to the risk we are willing to take. The more risk we can take, the more returns we will get. So the investment return is a function of our risk tolerance. The Kelly Formula, however, says returns don’t always go up when we take more risk, even if we can ignore the risk completely, and have a very good risk appetite: there is a maximum risk we should take, more risk taking will only bring worse returns. In other words, “volatility” is more than just the risk we have to experience during the process, or more than just the wider dispersion of possible returns; higher volatility may also reduce the eventual expected return. Why is that? That is because the returns of sequential investments multiply on each other, instead of “adding” onto each other. For example, if you lose 50% in the first year, you have to make 100% gain on the next year to get back even. It is (100% – 50%) * (100% + 100%) = 100%, rather than (50% + 100%) = 150%. In math terms, the returns are multiplicative, instead of additive. (The log-returns or log-assets are additive instead). This concept is very interesting and very useful, when we start to apply it to many financial decisions. For example, many years ago, I used to think that I should invest 100% on stocks since historically stocks had higher returns than bonds or bank CDs, and since I was very young, I shouldn’t be too concerned about the risks of stocks. That seems very logical, right? Well, not after you get familiar with the Kelly Formula. The fact is, if stocks are very volatile, 100% invested in stocks may not give your best returns even if the stocks do turn out to have better returns than bonds/CD’s, and even when we assume you don’t care about the risks at all. Let’s work through an example to better understand this: Suppose you had $100 at the beginning of 2008, and stock market dropped 50% and it became $50 at the beginning of 2009. Two years later, the stock market fully recovered, rose 140% and your asset got back to $120, therefore you had a 20% gain in 3 years. Very bumpy and scary roller-coaster ride indeed, but assuming you have very good risk tolerance, that didn’t matter much to you. What if you had 70% on stocks and 30% on bonds? At the beginning of 2009, because of the government’s monetary policy, the bond interest rate dropped significantly, and your bonds had a 20% return in 1 year, but your stocks had a 50% loss. Together, it is $70 * 0.5 + $30 * 1.2 = $71, or 29% total loss. At this point, you should do a rebalancing (assuming you rebalance every year), and get back to 70% stocks and 30% bonds, so you would sell some bonds and buy more stocks. After that, you would have $49.7 in stocks, and $21.3 in bonds. Then assuming 2 years later, stocks went up 140%, and bonds had a return of 0% during these 2 years, your total asset became $49.7 * 2.4 + $21.3 = $140.58. This is a total return of 40.58% in 3 years, which is much more than the 20% return in the 100% stock case. What is more interesting here is that both underlying assets (stock and bond) only had 20% return in 3 years, yet the portfolio had 40% return, much more than the return of any of the underlying assets. (See the “magic” of financial engineering can sometimes turn toads into princes!) Now it seems to be a no-brainer for you to always invest some of your capital in bonds? After all, if it gives you more return and less risk, why not? Not too fast. In the example above, I used 2008 – 2010 as an example, and my figures are hypothetical. After all, you won’t see a lot of 2008s happening down the road. That said, the basic reasoning here still applies: Reducing the volatility of a portfolio can also help to improve returns, not just reduce the risks. The ultimate decision of portfolio allocation depends on how risky the underlying asset is. Maybe 100% stocks is optimal, maybe not, but it really requires you to have a fairly accurate estimate of the future volatility of your stock assets. Is Kelly Bet The Optimal Bet? Another interesting property of Kelly Bet is that it is the “optimal bet”. Well, I just said it is the “maximum bet”, but why am I also calling it the “optimal bet”? The reality is that the “maximum bet” part of the theory is actually agreed upon by almost everyone: normally you never want to bet more than Kelly Bet, unless you were too conservative on estimating your winning odds. In other words, if you bet more than Kelly Bet, you are not just aggressive, you are “insane”, since it will bring higher risk AND worse performance too. But calling it “optimal bet” becomes much more controversial among investors and traders. The theory does show that it is indeed the optimal bet, but that has a lot assumptions attached to it, such as: the bet can be made frequently (not exactly true for long term investments), the bets have the same odds, the odds could be estimated accurately, and you could never lose 100% of your asset. As you can see, the first 3 conditions are not true for long term investments, and the last one is probably true if you have fairly good diversification and don’t use any leverage. This is where the theory diverts from reality, and why we have to be careful when assuming Kelly Bet is the optimal bet. If you want to learn more about Kelly Bet, you can check out my blogs here and here . Common Methods on Reducing Volatilities As I mentioned above, reducing volatilities is so important that it not only helps to reduce your risk and overcome your emotions, but can also help to improve your performance. Therefore, managing volatilities of a portfolio becomes a central topic of risk management and money management. A following question is: how can we reduce the volatility? As you will find out below, this is much more than just diversification. Diversification Despite all the caveats and potential drawbacks, diversification is still the most powerful concept in financial engineering on reducing the volatility. However, people sometimes either over-extend this concept or didn’t apply it in full scale. Diversification should not be just among stocks Normally, money managers often talk about how many stocks they should hold, or how big each position should be, such as whether each position should be 1%, 5% or 20% of the portfolio. However, diversification should not just be among the stocks you hold. First, stocks usually have high correlations, or we can call it “systematic risk”. If they are in the same sector and the same country, they will have even higher correlations. So when you have more than 7 – 20 stocks in your portfolio, additional stocks may not do much good to your portfolio at all. On the contrary, it may harm you more than help you, especially when you are a small investor. This is because over-diversification will spread you too thin, make you have less information edge over the stocks you own. It may also make your performance suffer because you have to put money into your less favorable ideas. One thing we should all realize is that investment is hard and highly competitive. For this reason, the chance that you can find a good idea is slim. You may get 1 or 2 really great ideas in a year, but expecting to get many great ideas is not realistic, even for those superinvestors. As Charlie Munger said, if you remove the top 20 best ideas Buffett had in the last 40 years, the rest of the ideas’ performance is not much better than the average index. In this sense, while having low volatility is important to improve performance, having higher expected returns is just as important. (I’d like to think higher expected return as “offense”, and lower risk as “defense”.) Also, diversification is not limited to just stocks, since it can be done in many other ways: Diversify over different asset classes Bonds, cash, commodities, gold and real estate are all asset classes that could be used for diversifying risks. Historically, bonds are one of the most favorable choices since they usually have negative correlation with stocks, which helps to reduce the volatility even more. But since bonds are not attractive right now due to all the QEs, cash and gold are probably good choices, too. Cash is stable, but has inflation risk. Gold has no inflation risk, and is especially helpful in doom scenarios, but its value is more dependent on supply-demand since it has no clear “fundamental value”. Diversify over different strategies This method may not be very practical for small investors, but money managers can often utilize different investment strategies to diversify the risks, such as allocating capital among trading strategies and investment strategies, so that they have less correlations. Or they can maintain short positions in addition to long positions. Downside Protection Is As Important Instead of diversification, value investors often make very restrict requirement on the downside protection on their stock picks. In Buffett’s words, the secret of investing is his: Rule No.1: Never lose money. Rule No.2: Never forget rule No.1. Here, “don’t lose money” doesn’t mean that there should be no loss at all, because that is certainly impossible. It only means “no significant loss” and you have to be really careful about protecting yourself from any significant downside on each individual stock you select. Usually this protection requires many of the following traits in the company you are investing in: Sufficient Margin Of Safety Low P/B ratio, and good tangible book value or liquidation value Durable competitive strength and low/reasonable P/E ratio Long product cycles Not overly dependent on one product, or one customer Low financial leverage and low operating leverage Good pricing power Recurring Revenue Good management Conservative accounting Non-cyclical industry Non-commodity product or has durable low-cost advantage “Certainty” is the basis of all investment theses As mentioned above, diversification has limited effectiveness and has significant drawbacks too. For this reason, successful value investors often use the downside protection of the business itself to reduce volatility. However, any investment thesis requires “certainty” or “information edge” as its basis. Without “certainty”, any conclusion could be built on imagination instead of facts. Therefore, to reduce volatility, investors have to devote their efforts to achieve an information edge and achieve high “certainty”, instead of just focusing on diversification. In other words, “certainty” and downside protection of each stock pick reduces the volatility of each position, and diversification reduces the overall volatility of the entire portfolio. Both of these methods are needed, but it is more of an art than science to find the balance between these two. In some sense, that also depends on personal style and personal strategies. Conclusion I remember Charlie Munger once said many smart people should better devote their talents to real engineering projects instead of financial engineering, since he thinks financial engineering doesn’t really generate much value for our society. While I am a fan of Munger, I don’t really agree with this particular comment. I believe understanding the math behind financial engineering can not only achieve better returns for our investments, but also help us to make better capital allocation decisions in general. There are many financial engineered products that are very useful to us, such index, index fund, ETFs, options, interest rate swaps, ABS or even the infamous CDOs. Many of these products used the powerful concept of “diversification”. It is undeniable that there are new problems coming up along with these new things, such as the loss of insight with over-diversification, or lack of incentives to ensure the quality. However, I would compare that with stock exchanges. While so many small investors unconsciously used the stock exchange as a casino (except that they wouldn’t bet all their savings in a casino like they did in the stock market), and sometimes lost all their lifetime savings (especially in immature markets, like the Chinese stock market), overall, stock exchanges still provided tremendous value for both businesses and investors. It does take time to get regulations in place to make it more mature though, as what we have seen in the US since 1930s. All in all, it is my opinion that financial engineering and the math behind it do provide good value to us, although it is also important to recognize its limitations and don’t lose our “common sense”.

SPHD: A Monthly Dividend ETF With A 3.5% Yield That Is Growing Stronger

Summary SPHD offers an excellent dividend yield of 3.5% with monthly payments. The ETF has a moderate expense ratio. The sector allocations look great and the volatility over the last few years has been lower than the domestic equity market. The PowerShares S&P 500 High Dividend Portfolio ETF (NYSEARCA: SPHD ) looks great. After readers suggested I take a look at the portfolio, I decided it was time to dive inside and see what I could find. This is a very solid ETF. Investors may quibble on whether the allocations are perfectly or merely good, but there is far more to like than to hold against the fund. As you’ll see in the article, I find the sector allocation to be a bigger selling point than the individual holdings. Expenses The expense ratio is a .30%. This is fairly mediocre for expense ratios in my estimation, but there have been quite a few funds coming up lately with expense rates that are downright excellent. Dividend Yield The dividend yield is currently running 3.50%. For the investor that wants a very strong dividend yield to support them in retirement, this should certainly qualify. Investors can create a stronger yield by selecting individual companies, but they are creating a high yield portfolio that is exposed to substantial risk of dividend cuts when they allocate aggressively to companies that are yielding materially higher than this portfolio. There are two other things to like about the dividend here. One is that the dividend is paid out on a monthly basis which many investors appreciate because it is easier for them to plan around. The other is that the 3.5% dividend yield is based on trailing dividends rather than forward dividends and the dividends have been moving slightly higher over the last year. The dividend went from around 9 and a half cents per month to over 10 cents per month. Holdings I grabbed the following chart to demonstrate the weight of the top 10 holdings: Seeing AT&T (NYSE: T ) and Verizon (NYSE: VZ ) with medium weights is one area where I tend to feel conflicted. Investors won’t see the Verizon in the chart, but I rarely find ETFs that only hold one. When I checked the rest of the holdings I found Verizon was represented with 2.22% of the portfolio. The dividend yields are great but the sector is becoming more competitive. On the upside any technology that actually makes them obsolete or at least incapable of growing earnings would be indicative of the investor having a lower cell phone bill, so there is another benefit to aligning the portfolio to match an investor’s individual expenditures. Honestly, is there any better way to pay your phone bill than with a dividend check from the phone company? This is a difficult one to come down on because I love the strategy of covering a cost with dividend income from the company, but I’m also concerned that Sprint (NYSE: S ) is offering a very viable competitive product. Their reception may be terrible in some cities, but they are great in Colorado Springs. Since the allocations are less than 5% of the portfolio combined, I think the representation here is pretty reasonable. I also see Realty Income Corp (NYSE: O ) as an easy choice for investors looking for solid growth in income. The triple net lease REIT has an excellent history of raising dividends. They pay their dividends monthly and have raised the dividend 81 times already. They have done an incredible job of executing their investment strategy and it is simpler than it seems. The REIT enters into net lease operations where the tenant is paying most of the operating costs. Realty Income Corporation is acting as an alternative format of financing for their tenant. Their strategy is so successful that they have been acquiring over a billion dollars in real estate each of the last few years. They already acquired almost a billion dollars in real estate in 2015. Sectors Heavy allocation to utilities makes sense for an equity fund seeking lower total volatility levels. The utility companies have a tendency to be partially correlated to equity and partially correlated to bonds which creates a method for a pure equity ETF to reduce volatility by incorporating some exposure that is very similar to bonds. For investors with a diversified portfolio, that means this fund may not get as large of a benefit from being combined with treasuries and other long duration bonds as a total market portfolio would get. Regardless, with investors needing stronger yields in retirement and often going light on bonds in favor of equity, this would be a more rational allocation model than simply going with full market exposure. The allocation to financials provides the shareholders with exposure to REITs that would fall with utilities when rates go up, but it also gives them access to banks that would benefit from higher rates paid on excess reserves. The combination works fairly well to create a portfolio with lower volatility. The heavy allocations to consumer staples also makes sense in that context since consumer staples tend to be a solid sector for taking smaller losses during a recession. I was a little curious about their decision to put 10% into industrials, but when I looked at the individual holdings for the sector it made sense. While General Electric (NYSE: GE ) is seeing their share prices just getting back to where they before the crash, their still offer a sold 3% yield. Volatility Measured since October 2012, this fund has demonstrated annualized volatility of 10.9% compared to 12.6% for the S&P 500. The beta on the fund has been a mere .75. While the fund has not kept up with the S&P 500, it is a very attractive allocation strategy with the market at fairly high valuation levels. For the investor that would like to reduce their risk and is willing to accept a lower long term projected return, this fund fits the bill. If market prices had fallen by 40%, I would try to look at more aggressive allocations. When prices still seem high, I prefer using defensive allocations and this fund offers a great deal of them. Conclusion All around this looks like a solid fund. The only thing I can find not to be excited about is the expense ratio. Even there, the ratio isn’t terrible. It is simply higher than what I am used to paying as I favor the Vanguard and Schwab ETFs. If this fund got larger and dropped the expense ratio, it would be absolutely excellent. I think that might be a viable option for the fund’s sponsor as well since the strong yield and monthly payment with a low expense ratio would create enough demand to warrant significantly more shares of this ETF being created.

VGHCX – An Investment Pick In The Health Care Sector

Summary Is this a good time to invest in Health Care Sector? What are some trends in the health care sector? How can investors capitalize on the health care trends to make good investment decisions? All investors have considered investing in specific sectors to bolster the return on investment portfolio. This approach while increasing the risk of the overall portfolio also has the potential to magnify returns if the sector performs well. Health care, considered as a defensive sector will likely outperform many other sectors due to a variety of reasons- aging baby boomers who are likely to need more care, increasing life expectancy, ever pervasive need to develop drugs to treat diseases, cutting edge innovations in medicines and state of the art medical equipments. According to an article in Forbes, health care spending per capita in US is around $10,000 this year with a total of $3.2 trillion in national health care expenditure. Here is my favorite pick in the health care industry: Vanguard Health Care Sector Fund (MUTF: VGHCX ): (click to enlarge) Source Data: Vanguard.com Key performance measures NAV Assets Expense ratio PE ratio $225.21 $48 B .34 37 VGHCX is well diversified fund in the health care sector with a good mix of investments in pharmaceuticals, bio technology, medical equipment companies, managed health care and health care facilities. The largest investment is in pharmaceutical firms which constitute about 45% of the portfolio. The fund focuses on well established large cap companies with average market capitalization around 45 B. Some of its top holdings include Bristol Myers Squibb (NYSE: BMY ), Allergan (NYSE: AGN ), Ely Lily (NYSE: LLY ), United Health Group (NYSE: UNH ), Merck &Co (NYSE: MRK ). About 80% of its portfolio is allocated to companies in US and the remaining 20% is invested in other countries. The foreign holding includes well established companies such as Roche Holdings and Novartis (NYSE: NVS ) based in Switzerland, Sanofi (NYSE: SNY ) located in France and Astra Zenaca (NYSE: AZN ) in United Kingdom. The expense ratio of .34 is very low compared to other healthcare funds. The fund is actively managed with a low turnover ratio of 20%. The turnover ratio indicates the number of times the fund manager buys/sells the securities within the fund. The low turnover ratio will result in lower transaction costs and higher returns to fund holders in the long run. It also reflects the expertise of the fund manager in picking companies with great growth potential and holding for longer periods as opposed to trading frequently. The average annual return on the fund has been around 17.28% since the fund’s inception in 1984 and well above the industry average. According to Vanguard interactive chart, an investment of $10,000 in 2005 would now be worth around $35000 in 2015. This return includes the impact of US and worldwide recession during 2007 to 2009. The total distributions including dividends, Short term, and Long term capital gain was $19 in 2014 which amounted to approximately 8% of NAV. According to Vanguard website, the realized gain as of September 2015 was 4.32% of NAV and the unrealized price appreciation of the fund was a whopping 38%. The median market cap of the assets within the fund is 42.8 billion with a total of 83 holdings. The PE ratio of 37 seems high compared to the industry average (as measured by the MSCI ACWI Health care index) of 24.4 as of October 2015. The health care sector has been characterized by blockbuster mergers/acquisitions, collaborative deals among big pharmaceuticals to develop the next breakthrough treatments for diseases. According to the Pharmaceuticals and Life Sciences insights by PWC.com, there were a total of 59 deals with a value of 67.6 billion during 2015. The low interest rate environment has fuelled a surge in mergers/acquisitions as well as organic growth within the health care sector in US and around the world. The rising share prices have facilitated mergers by enabling companies to use stock as a currency for acquisitions. The VGHCX fund has significant stakes in many of the pharmaceutical/biotech firms companies involved in mutually beneficial deals/consolidations. These deals are expected to shore up the future cash flows considerably for the portfolio companies within the fund and boost the return to holders of VGHCX fund. Highlights of Mergers/Acquisitions/ Partnership deals on top holdings companies within the VGHCX Fund: Actavis, a Dublin based pharmaceutical acquired Allergan for $70.5 billion creating one of the world’s largest pharmaceutical companies. The combined firm anticipated revenues around $23 billion during 2015. Some excerpts from Actavis.com Supporting the growth of this innovative industry model is our strategically focused R&D engine, built on novel compounds in specialty and primary care markets where there is significant unmet medical need, and fueled by approximately $1.7 billion in annual investment. With an innovative product development portfolio exceeding 20 near-term projects and a world-class generics pipeline, which continues to hold an industry-leading position in First-to-File opportunities in the U.S. and more than 1,000 marketing authorizations globally, we are uniquely positioned within our industry to ensure our development activities support sustainable long-term organic growth. Subsequently, Teva Pharmaceutical (NYSE: TEVA ) an Israeli based pharmaceutical company acquired the generics unit from Allergan for $40.5 billion thereby giving the much needed cash infusion to Allergan to reduce its debt level according an article in Wall Street Journal. Bristol Myers Squibb a market leader in oncology recently acquired Flexus Biosciences a privately held biotechnology firm company which specialized in discovery and development of cancer medications for $1.25 billion. Eli Lily acquired Elanco, animal health division of Novartis for $5.4 billion partly funded by cash and debt. According to Eli Lily: Upon completion of the acquisition, Elanco will be the second-largest animal health company in terms of global revenue, will solidify its number two ranking in the U.S., and improve its position in Europe and the rest of the world. With a presence in approximately 40 countries and 2013 revenue of approximately $1.1 billion, Novartis Animal Health is focused on developing better ways to prevent and treat diseases in pets, farm animals and farmed fish. Lilly will acquire Novartis Animal Health’s nine manufacturing sites, six dedicated research and development facilities, a global commercial infrastructure with a portfolio of approximately 600 products, a robust pipeline with more than 40 projects in development, and an experienced team of more than 3,000 employees. Regeneron Pharmaceuticals has entered into collaborative deals with Bayer Health care for treatment of eye diseases, according to Regeneron.com. The companies will share the cost of developing the products as well as the profits. Renegeron and Sanofi have entered into immune-oncology collaboration with Sanofi providing 165 million for research and development of products in this field. Investment Risks: The risks are high since all stocks are concentrated in one sector. The big pharmaceutical firms face fierce competition with each other in coming up with a major breakthrough in treatments. If FDA does not approve the drugs, the biopharmaceutical companies are likely to experience a steep decline in revenues and earnings. Many of the firms may face litigations if the patient experiences adverse side effects due to the drug usage. The biopharmaceutical may experience a sharp decline in revenues after the patents expire. Future Outlook: According to American Public Health Association (APHA) majority of the deaths in US are related to heart disease, diabetes, obesity, high blood pressure and cancer. Money is spent more on treatments rather in prevention. It is hoped that this trend will be reversed as more and more people have health insurance and can afford to spend money on preventive health care. The Affordable Care Act, 2010 has the goal of expanding insurance coverage in US and it is hoped that the coverage will reach 24 million by 2023. The increased health care coverage will likely result in greater doctor and hospital visits. The average life expectancy is around 79 in United States according to World Bank estimates. Baby boomers are expected to spend substantially on health care treatments while Millinnials are likely to spend on preventive health care. Being the recipient of the additional funds spent by Baby boomers, Millennials, and Generation X, the Health Care Sector will continue its stellar performance well into the future. The VGHCX fund which has stakes in well established companies large cap companies will likely reap the benefits of trends in health care industry. With a majority of investments in large stable pharmaceuticals with a median market cap of 40 billion, the VGHCX fund will likely continue its trend of double digit growth rate in earnings and revenues. The fund is trading at approximately 8% below its all time high. With a PE ratio above industry average, the fund still looks expensive. In my opinion, investors can monitor the NAV and add positions when there is a temporary pull back of at least 10% to 15% of NAV. The markets are volatile and there are plenty of opportunities for investors to add positions on a day the market indexes slump. This actively managed fund with the optimal mix of winning companies within the health care sector will be a great investment choice for the long term.