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Tax-Free Income For Those Who Need It Most: California Municipal Bond CEFs

Summary California’s tax-free income investing is covered by 22 closed-end funds. These present a diverse array of offerings varying in distribution, leverage and all aspects of portfolio composition. In this article I take a look at all 22 of the funds. I look at municipal bond closed-end funds periodically and try to keep readers up to date on the category as changes occur . In doing so, I focus specifically on national funds because I feel it interests a broader audience than any single state fund. Being a Californian I do watch the California funds carefully, and the bulk of my muni bond fund holdings are California state funds. But I’ve not taken the time to write up my research in these funds because I thought the broad interest would not be there. I get frequent requests for coverage of state muni bond funds, especially the high-tax, high-population states, California and New York. So, with this effort, I’ll put together some of my results on California state municipal bond tax-free CEFs. These funds invest exclusively in California municipal bonds and are, therefore, exempt from both federal and state taxes. My fellow Californians appreciate how much it can add to the value of a fund’s distributions when you take away the tax bite from the country’s highest state tax levels. Several years ago, California allowed an exemption for the California portion of national muni bond funds, but as I understand current tax policy in order for a fund’s distributions to be exempt from California taxes, it must have at least 50% of its holdings from eligible California holdings. Why Single State Muni Bonds? Determining how much advantage one gets from federal and state tax-exempt income can be opaque. Fund sponsors and data aggregators tend to report tax-equivalent returns based on the highest marginal brackets. Few of us qualify at that level, so the reported (or should I say, advertised?) data is near meaningless. It is fairly straightforward to find a tax-equivalent return for federal taxes; one simply has to plug in the marginal rate for a simple calculation. But for state taxes it is more complex. For one thing federal and state marginal rate increments do not correspond. For another, in California at least, federal tax is a deductible, which means one has to adjust the income from the muni bonds to take the federal exemption into consideration. I am not even remotely a tax expert, but real tax experts at Eaton Vance have created an excellent calculator for determining tax equivalence for national and state tax funds based on an individual’s filing status and income level. To make it more useful, it includes equivalent yields not just for ordinary income, but for government bonds, for which interest is tax-exempt in California, qualified dividends, and long- and short-term capital gains. You can find this useful resource here . I know of nothing more comprehensive. I’ve run up a chart showing taxable equivalents for distribution yields of California muni bond funds. This only covers the case for married filing jointly status, so do check out the EV site for your precise situation. The California Municipal Bond CEFs A good thing about trying to get a handle on California muni bond CEFs is that there is a manageable number to deal with. There are 99 national funds which makes ferreting out comparative information not available from screeners and data aggregators a daunting task. I am not aware of any screeners that let me filter on important metrics like portfolio duration or credit quality or AMT percentage. For me, this mean filtering on metrics like discount status, distributions, Z-scores, maturity, leverage and the like to narrow the pool and then try to fill in the gaps. Things get overlooked with this approach and one of the advantages I’ve found from making my results public here is that some very knowledgeable readers will pass along some of their favorites that I overlooked using this approach. With only 22 funds for California munis, one can dig out these data manually with a reasonable investment of effort. Indeed, it’s worth listing all 22 of them here, along with some key characteristics of the funds. First, the funds: Alliance California Municipal Income Fund (NYSE: AKP ) Blackrock California Municipal Income Trust (NYSE: BFZ ) Blackrock California Municipal 2018 Term Trust (NYSE: BJZ ) MFS California Municipal Fund (NYSEMKT: CCA ) Eaton Vance California Municipal Income Trust (NYSEMKT: CEV ) Eaton Vance California Municipal Bond Fund II (NYSEMKT: EIA ) Eaton Vance California Municipal Bond Fund (NYSEMKT: EVM ) Blackrock Muniyield California Quality Fund, Inc. (NYSE: MCA ) Blackrock Muniholdings California Quality Fund, Inc. (NYSE: MUC ) Blackrock Muniyield California Fund, Inc. (NYSE: MYC ) Neuberger Berman California Intermediate Municipal Fund Inc (NYSEMKT: NBW ) Nuveen California Dividend Advantage Municipal Fund (NYSE: NAC ) Nuveen California Municipal Value Fund Inc (NYSE: NCA ) Nuveen California Municipal Value Fund 2 (NYSEMKT: NCB ) Nuveen California AMT-Free Municipal Income Fund (NYSE: NKX ) Nuveen California Dividend Advantage Municipal Fund 2 (NYSEMKT: NVX ) Nuveen California Select Tax Free Income Portfolio (NYSE: NXC ) Nuveen California Dividend Advantage Municipal Fund 3 (NYSEMKT: NZH ) Pimco California Municipal Income Fund II (NYSE: PCK ) Pimco California Municipal Income Fund (NYSE: PCQ ) Pimco California Municipal Income Fund III (NYSE: PZC ) Invesco California Value Municipal Income Trust (NYSE: VCV ) Sorted by market cap the category breaks down like this: (click to enlarge) Some of the funds at the right side of this chart can present liquidity issues. I tend to put limit, all-or-none orders in when I bid on CEFs. I was unable to buy EIA at terms that might not have been a problem for more liquid funds. Leverage is an important driver of high distribution income from muni bond funds. People will fret about leverage and the threat of rising rates, but that’s how these fund deliver better than 5% yields from such low yielding assets. For those who dread the thought, there are 4 minimally leveraged funds in the mix. (click to enlarge) The whole point of holding any income fund, taxable or tax-free, is, of course, income. So, what sort of income can we expect from the California muni bonds CEFs. Here is a chart of current distribution yields at market price and NAV. (click to enlarge) Note that the two high-yielding PIMCO funds at the left have market yields below their NAV distributions. This is, of course, a reflection of their premium valuations. For most of the remaining funds their discounts give a boost (albeit smallish right now) to their yields. So, let’s turn to discounts and premiums. Seventeen of the 22 funds currently hold a discount. True to PIMCO form, their 3 funds have premium valuations. This is a recurring story throughout fixed-income CEF space. PIMCO, by application of their secret sauce, manages to generate NAV yields appreciably above their peers. Investors respond by bidding the funds up into premium territory, reducing the yields from NAV, but keeping them above the pack at market price. Interestingly, the other premium funds are two low-yielding, low-leverage funds from Nuveen, NCA and NXC. BIZ, the fund with the skimpiest discount is the fund that carries the least leverage. It appears investors are willing to pay premium prices and accept lower distributions (see distributions chart above) to forego leverage. More than three-quarters of the funds have discounts, but for each of them the discount is shrinking. This is something one might infer from the RSI data above; a look at Z-scores for three months confirms it. (click to enlarge) Z-Score is a measure of how far the current discount/premium varies from the average discount/premium for a time period. A negative Z-score indicates that the discount has deepened relative to the mean. Not one of these funds has a negative Z-Score for the past three months. The most accessible way to approach the Z-statistic is to read it as the number of standard deviations the current value is above or below the mean for the period. Seventeen funds are more than a standard deviation away from the mean discount/premium. Thirteen are more than two standard deviations away, and one, NXC, is more than 3.5 standard deviations above its mean value. The message here, coupled with the RSI data at the top, is that now is not a timely entry point for California muni bond CEFs. For the record, here are the 6 and 12 month Z-scores using the same sort to facilitate comparisons. (click to enlarge) It was not so long ago that California muni bond funds were a great bargain. Deep discounts were the norm. Funds were discounted to the extent that it was possible to buy funds that were returning higher yields on market price than comparable national muni bond CEFs. What changed? To answer this we need to understand what was driving those bargains. Two California municipalities were in the news as bordering on bankruptcy. The larger of the two, Stockton, is a good size city and the press was full of doom and gloom for the fiscal condition of the Golden State. At time, I began writing about muni bond CEFs and numerous commenters referenced Stockton and put California in the same category as Puerto Rico on the at-risk scale. Predictably, holders of California CEFs jumped ship in droves. Bargains were the order of the day. At the time I argued that 1) California was in no worse fiscal condition than any other large, diverse and complex state; and 2) muni bond defaults were so rare as to be negligible. It took about a year or so, but investors have decided that California may not be so bad after all. What is worrisome to a less skittish CEF buyer is whether or not the current upsurge is an overreaction. I depend on my California muni CEFs for income but I am seriously considering taking profits here with an eye to coming back in when the prices compensate yet again in the next direction. That’s part of my recent interest in national muni bonds as I look for alternative income sources. Oh, what’s that I hear. Something about hand waving on that muni defaults comment? Ok, here’s some evidence from Oppenheimer’s year-end Chart Book comparing muni bond defaults to corporate defaults for BBB rated bonds. Next time you hear about how muni bonds are ready to crash and burn remember this chart: (click to enlarge) NAV Yield and Discount Trend As those who follow my work on munis are aware, I like to look at the relationship between NAV Yield and Discount/Premium. One factor that contributes to a fund finding its market discount or premium is yield on NAV. Investors tend to drive fund prices toward an equilibrium on market yield by price up funds with high NAV yields and pricing down funds with low NAV yields (see PIMCO discussion above for extreme examples). We can plot that relationship thusly: (click to enlarge) I’ve omitted the low leverage funds from this chart. The r2 is very high (0.88) indicating the strength of the relationship in this case. By this indicator funds that fall below the trendline tend to be better priced than those above it. It’s telling us to look closely at VCV, NZH, EVM, EIA, and perhaps, NAC. I’ll fit these funds into other metrics as I proceed. Portfolio Composition This raises the issue of portfolio compositions. Two components are of special interest in this regard: Duration and Credit Quality. This table is from Morningstar’s analyses of the funds. The effective durations are unadjusted and adjusted for leverage. Average weighted credit rating is based on Morningstar’s weightings which gives higher weight to lower quality bonds. It varies from what you might see elsewhere, but it is consistent from fund to fund, unlike what you might see elsewhere. It tends, like much of what Morningstar puts out, to present the most conservative case. (click to enlarge) I’ve included discount and distribution yield here to show relationships. I’ve also put in a column showing Morningstar’s category for each fund to point out how unreliable such categorizations can be. While BIZ, one of the two intermediate funds, does have the shortest adjusted duration, NCB, the other, is well into the upper middle of the pack. EIA, a long fund according to Morningstar has the shortest unadjusted duration and lags BIZ by a trivial 0.23 when adjusted for its leverage. But I digress, let’s go on to credit quality. I’ve sorted the table on credit quality. One might expect yield to reflect that sort but it doesn’t. PCK with a BB+ portfolio has the highest yield here, and that’s with a 12% premium which means the managers are generating 7.4% yield from California muni bonds. It does, however, also somewhat typical for high-premium, high-yield PIMCO funds, post negative undistributed net investment income. PCK’s UNII runs about -7.2% of its annual distribution (at market) or somewhat less than a single month’s premium. While not at a level that puts up worrisome red flags, it is the highest in the category. The fund last cut its distribution in April 2014 (-14%). Two Blackrock funds, MCA and MYC, have the strongest credit quality with average ratings of AA-. They fall mid-pack for distribution, near the top for leverage, and about the middle for adjusted duration. For anyone concerned about credit risk, they may represent the best choice. A step down the credit quality scale is NBW which shares a BB+ rating with PCK. It has a moderate discount of -3%, a mid level yield of 5.47%, and the second highest leverage (41.02% to PCK’s high value of 41.12%) in the category. It pays more than a point less than PCK, slightly less then the better-rated portfolios from MCA and MYC, so I see no reason one would purchase it at this time. Dropping down to BBB+ takes us to another Blackrock fund, BFZ. It offers a solid distribution yields of 5.62%, medium low adjusted duration and a discount of -2.34%. Eaton Vance’s EIA holds one of several BBB rated portfolios and generates the highest yield of the set. It does so with an impressively short leverage-adjusted duration (3.7) second only to the unleveraged BIZ. For all but the most yield-hungry or credit-wary, it should be the choice of group. I’ve tried to summarize portfolio compositions in this chart. Funds are grouped by weighted average credit rating and scored on the basis of distribution yield. The dot size represents the level of leverage. (click to enlarge) From this view, MCA, MYC, PCK look like the top choices. But this view does not factor in PCK’s premium. Nor does it include our knowledge of that negative UNII. So I’d go with Blackrock’s offerings with the race going to MCA on the basis of those few basis points of higher yield generated by its deeper discount. Both of those factors could change in a day, so let’s call them a wash. BFZ could be considered next along with EIA and EVM. BFZ offers a better credit quality (BBB+ to BBB) but trails a bit in yield. EIA wins handily on effective duration with BFZ near and EVM trailing slightly. Beyond these fund, one is looking primarily for high yield, so there’s PCZ with its 12% premium, or Invesco’s VCV with a -6.1% discount. One would have to be satisfied that PZC’s quarter point of yield justified the premium purchase to chose it over VCV. Finally, for an investor who puts yield second to leverage (or lack of leverage), the two choices would seem to be Nuveen’s NCA or NCB. I did not try to find AMT liability for all of the funds but the few I’ve singled out range from AMT free to having moderate levels of their income subject to AMT. The Eaton Vance funds (EIA and EVM) are AMT free as are the PIMCO funds (PCK, PCQ and PZC). Blackrock’s funds do have AMT liability: BFZ (1.43%), MYC (3.53%), MCA (4.70%). Invesco’s VCV has 4.56% subject to AMT and for Neuberger Berman’s NBW it’s 5.27%. The low leverage funds top the list with NCA at 11.58% and NCB at 6.27%. Summing Up California Muni Bond CEFs are likely overbought and investors who are inclined to trade funds as discounts and premiums rise and fall should likely be looking to sell rather than make purchases at this time. Investors interested in opening or expanding long term positions in California tax-free income have some solid choice depending on one’s priorities. EIA with is high quality portfolio and short durations is a strong contender as is its stable mate EVM. MCA and MYC offer the lowest credit risk and give up only trivial amounts on yield. Other funds with solid reasons to own and hold include VCV for high yield, NBW for its portfolio quality, and NCA and NCB for low leverage. PCK is a solid choice for someone willing to overlook the premium and the negative UNII. It’s not for me but PIMCO’s premium funds have their staunch advocates.

The Importance Of Emphasizing Quality And Financial Health In Your Stock Holdings

A majority of stock fund managers want corporations to improve their financial health as opposed to rewarding shareholders through buybacks and dividends. Unfortunately, the ability for corporations to service existing debt is at its lowest point since 2009. Companies with the highest-rated financial health have outperformed SPY in 2015, whereas buyback “achieving” corporations have been sliding. According to a recent Bank of America Merrill Lynch survey, a majority of stock fund managers want corporations to improve their financial health as opposed to rewarding shareholders through buybacks and dividends. That has not happened since the earliest stages of the economic recovery. Why are asset managers, myself included, expressing concern about what companies do with their money? They’ve taken on too much debt. They are leveraged to the hilt . In fact, corporations owe more interest on their debt than at any prior point in history. That’s not a problem, you argue. The only thing that matters for “credit-worthy” businesses is their ability to service their obligations. And the Federal Reserve will remain very accommodating for many years to come. Unfortunately, the ability for corporations to service existing debt (a.k.a. “interest coverage”) is at its lowest point since 2009. Imagine that. In spite of a Fed that has kept overnight lending rates near zero for seven years, companies face the same challenge with debt servicing today as they had back in the recession. Worse yet, what is the probable outcome for corporations if Janet Yellen and her Fed colleagues actually hike borrowing costs in the near future? Perhaps you are skeptical about the notion that public corporations might stumble with respect to growing their businesses while paying back existing debts. Then you might want to look at the changing landscape for companies that reward shareholders with stock buybacks. At the start of the current recovery up through the end of last year (12/31/2014), the PowerShares Buyback Achievers Portfolio ETF (NYSEARCA: PKW ) outperformed the SPDR S&P 500 Trust ETF (NYSEARCA: SPY ) by a landslide (i.e., 187% to 125%). Since the start of 2015, however, companies borrowing to buy back their stock shares have lost significant momentum. The declining PKW:SPY price ratio below demonstrates the shift from confidence to concern. Why should corporations that are limiting stock supply and increasing demand through their buybacks see their share underperform? In essence, there’s trepidation that some corporations have borrowed beyond sensible leverage ratios and simultaneously puffed up their earnings in ways that may not reflect organic growth. Keep in mind, business loans as a percentage of GDP are higher now than at August of 2000 and at August of 2007. The use of leverage by households, government, financial companies and non-financial companies was certainly out of control at those moments in history. What’s more, the leverage extremes of the past led to credit cycle and business cycle contractions. It follows that it may be reasonable to assume that credit contraction is likely to occur soon enough. In fact, extremes in the use of leverage tend to downshift at the least opportune times. Fewer borrowed dollars would mean less money for productive purposes (e.g., plants, equipment, human resources, research, etc.) or for immediate investor benefit (e.g., share buybacks, dividend increases, etc.). Some may believe that central bankers are more prepared for a severe pullback in credit today. Perhaps they would turn toward an even larger open-ended quantitative easing (QE) program or implement a policy of negative interest rates. The only problem is, corporate bond issuers are already seeing diminishing benefits of lower yields. The Fed, the Bank of Japan, The European Central Bank may be eager to promote lending at a time when they see a need for more stimulus, but it may not matter if households and corporations are fearful of additional borrowing. It should come as no surprise, then, that companies with the highest-rated financial health have outperformed SPY in 2015. Whereas buyback “achieving” corporations have been sliding via the PKW:SPY price ratio above, the iShares MSCI USA Quality Factor ETF (NYSEARCA: QUAL ):SPY price ratio has been rising throughout the year. Binge borrowing by corporations may not be a death knell for the bull market in stocks. Nevertheless, when one factors earnings declines and revenue declines into diminishing benefits from ultra-low borrowing costs, one may find it less lucrative to buy every dip. Disclosure: Gary Gordon, MS, CFP is the president of Pacific Park Financial, Inc., a Registered Investment Adviser with the SEC. Gary Gordon, Pacific Park Financial, Inc, and/or its clients may hold positions in the ETFs, mutual funds, and/or any investment asset mentioned above. The commentary does not constitute individualized investment advice. The opinions offered herein are not personalized recommendations to buy, sell or hold securities. At times, issuers of exchange-traded products compensate Pacific Park Financial, Inc. or its subsidiaries for advertising at the ETF Expert web site. ETF Expert content is created independently of any advertising relationships.

Portfolio Allocations: Bet Sizing

The math that dictates optimal portfolio allocations is complicated and an overly simplistic approach introduces a lot of unnecessary risk. The math of “gambling” and the math of investing share a lot of similarities. I believe the math presented below is equally applicable to both worlds. While EV (Expected Value) is a critical concept, it is meaningless without the concept of EG (Expected Growth). Chip Kelly is not the guy the “Kelly Criterion” is named after, but his presence creates interesting football betting opportunities. As a guy who many would consider to be a “professional gambler,” the concept of bet sizing has been something that I have spent a lot of time thinking about. I firmly believe trading stocks and derivatives for great portfolio managers is not all that different from playing poker for elite poker players. Individual investments for a portfolio manager and individual bets of a poker player (or elite sports handicapper) may be extremely risky, but the entire set of investments that make up a portfolio or long series of bets over time by a “professional gambler” are likely to yield a high return with a relatively low risk over the long run. This article is in response to an Instablog written by one of the most interesting contributors on this site, Chris DeMuth . He gives a relatively simple methodology of how to allocate capital. He presents the basic premise that he will invest around 1.25% of his portfolio in an investment he likes and will increase his position in the stock if he continues to love it as the price declines. He will continue to add to this position until a maximum of 10% of his portfolio is allocated to the individual investment. Adding to an investment that is becoming more undervalued relative to its fair market value makes a lot of sense. However, the exact portfolio allocations he suggests seem to be quite arbitrarily chosen instead of meticulously calculated. Based on my user name, it is probably clear that I have spent a lot of time in my life thinking about the fancy math of endeavors most would consider to be reckless gambling. I would like to introduce the idea of the Kelly Criterion, the most fundamental formula for elite sports gamblers. You can read about it here . What this magic formula does is tell you how much of your portfolio (bankroll) you should invest (bet) on a particular investment in order to maximize the growth of your portfolio given your estimate of the probability of winning and the odds received on the wager. The formula is written below: Every investor (bettor) is familiar with the concept of EV (Expected Value). Everyone knows that positive EV bets are wonderful. However, there is a corresponding concept that is much less well understood. It is the idea of Expected Growth, and frankly, it is equally important to understand as Expected Value when thinking about portfolio allocations. Let’s consider an investment where you are allowed to bet on a game of flipping quarters. The odds of picking a winning bet are 50% when flipping a quarter one time. Let’s also assume that in this generous game that for each flip of the quarter, you are getting a +200 payout. For those of you not familiar with common sports gambling notation, this means that you are given 2-1 on your wager. If you wager $1 on this bet and lose, you will lose $1. However, if you win, you will receive back $3 ($1 for your initial investment and a $2 profit). Better yet, let us assume that there are no caps on how much we are allowed to bet. This is a wonderful game that I would love to play forever everyday if it were readily available. Let’s now further assume you have a bankroll of $1,000,000. You are allowed to play this game only two times. In this game, there are four distinct possible outcomes (the sample space) that each have the same probability of occurring. The 4 possible outcomes are as follows: Win both the first and second bets. Win the first bet, lose the second bet. Lose the first bet, win the second bet. Lose both the first and second bets. Let’s assume that you are conservative and wager 1% of your bankroll on each coin flip. These are the possible outcomes of the size of your bankroll after playing the game of 2 quarter flips. Bankroll = $1,000,000 x (1 + (2 * 0.01)) x (1 + (2 * 0.01)) = $1,040,400 Bankroll = $1,000,000 x (1 + (2 * 0.01)) x (1 – (1 * 0.01)) = $1,009,800 Bankroll = $1,000,000 x (1 – (1 * 0.01)) x (1 + (2 * 0.01)) = $1,009,800 Bankroll = $1,000,000 x (1 – (1 * 0.01)) x (1 – (1 * 0.01)) = $980,100 Since each of these results is equally likely, the Expected Value of the outcome of these sequential bets is a profit of $10,025 (or 1.0025%). Expected Growth (EG) is a little bit more tricky. In order to figure it out (without having the formula in front of you), you must see what the expected outcome is. Since the odds of the game are always 50/50 for each coin flip, the expected outcome is simply winning once for each time you lose. Since we are flipping the coin twice, the expected outcome is to win once and lose once. The order that you win or lose doesn’t matter as the bankroll ends up at the same number either way in this game. The bankroll, based on the calculations above, in the expected outcome is $1,009,800, which is a profit of $9,800 (or 0.98%). This 0.98% is the EG. For those that are interested in generalized equations, here they are: Bankroll after Expected Outcome = (Initial Bankroll) * (1 + (Decimal Odds – 1) * (Bet Size / Initial Bankroll))p * (1 – (Bet Size / Initial Bankroll))(1 – p) EG = (1 + (Decimal odds – 1) * (Bet Size / Initial Bankroll))p * (1 – (Bet Size / Initial Bankroll))(1-p) – 1 EV = ((p * Decimal Odds) – 1) * (Bet Size / Initial Bankroll) where p is the probability of winning Let’s look at a fun example of playing that original game but instead of betting 1% of your bankroll on each coin flip, you want to make a bet with a higher EV and bet 90% of your bankroll. (For those of you still reading at this point, that is far greater than what the Kelly criterion says you should bet.) The 4 possible outcomes are as follows again: Win both the first and second bets. Win the first bet, lose the second bet. Lose the first bet, win the second bet. Lose both the first and second bets. Bankroll = $1,000,000 x (1 + (2 * 0.90)) x (1 + (2 * 0.90)) = $7,840,000 Bankroll = $1,000,000 x (1 + (2 * 0.90)) x (1 – (1 * 0.90)) = $280,000 Bankroll = $1,000,000 x (1 – (1 * 0.90)) x (1 + (2 * 0.90)) = $280,000 Bankroll = $1,000,000 x (1 – (1 * 0.90)) x (1 – (1 * 0.90)) = $10,000 Since each of the 4 outcomes is equally likely, that yields an EV of $2,102,500 or a profit of $1,102,500 (or 110.25%). However, the EG here is a loss of 74%! That means that although you would be making bets with higher expected value, you would end up with (significantly) worse expected growth. In fact, you now expect a significant shrink in the size of your portfolio (or bankroll). Extending this logic out further, if you were to go “all in” on every single bet even if the coin were weighted in a manner such that you win 99.999999999% of the time, the EG = -100% if you are allowed to flip the coin infinite many times despite the fact that your EV would be exploding to infinity. The math of investing isn’t as simple as winning and losing as in the case, I present above. You get to input distributions of possible results with probability distributions of those results. In the end, you get to the indisputable truth that BET SIZING MATTERS (portfolio allocation sizing matters). The math gets way more complicated than this and frankly, I don’t truly understand it yet. The key takeaways from this fun math end up being quite intuitive: The better the investment (in terms of expected return and likelihood of success), the greater the percentage of your portfolio that you should allocate to this investment. If you overbet (oh what a horrible screen name to have for this discussion) or underbet, you will not maximize your expected growth. If you underbet in a +EV situation, you still will expect to grow your portfolio. If you overbet in a +EV situation, expected growth of your portfolio can be positive or negative. The penalty of underbetting (in general) is less severe than the penalty of overbetting. While I think the guidelines Chris DeMuth lays out are not necessarily all that bad in practice, I would caution taking an overly simplistic approach to a (very) complex problem.