Merger Arbitrage Funds as Portfolio Diversifiers
alternatives, analysis, app, asset allocation, correlation, portfolio

A recent article in The Wall Street Journal’s Investing in Funds & ETFs report discusses merger arbitrage mutual funds. According to the article, such funds

…may offer an attractive way to diversify away from the risks of stocks or bonds …[but] can’t replace bonds, because their returns aren’t certain and come mostly through any price appreciation, not yield. But held in tandem with bonds, they can offer a way to hedge against interest-rate risk and might cushion part of a portfolio against stock-market volatility

Let’s take a closer look at these statements with the help of a recently introduced Alpholio™ App for Android, and specifically its Portfolio, Correlation, Total Return and Efficient Frontier services. For the purposes of this analysis, the base portfolio consists of 60% SPDR® S&P 500® ETF (SPY) and 40% of the iShares Core U.S. Aggregate Bond ETF (AGG), i.e. a traditional balanced mix of stocks and bonds. Here is the baseline chart with statistics generated from total monthly returns of both ETFs and quarterly rebalancing of the portfolio:

Portfolio 60% SPY + 40% AGG

The reason why the beta of this portfolio is not exactly 0.6 (i.e. equal to the 60% weight of the SPY) is threefold. Alpholio™ uses a broader definition of “the market” than just the S&P 500® index. Also, the correlation between the market and AGG is not zero. Finally, the portfolio is rebalanced quarterly, not monthly, which can lead to a temporary divergence of SPY/AGG weights from the original 60/40% level.

For reference, in the same time frame a portfolio consisting of just the SPY would have an annualized return of 8.52% with a standard deviation of 14.25%, Sharpe ratio of 0.55 and maximum drawdown of 50.8%. Adding AGG to such an equity-only portfolio decreases its return but reduces its volatility even more, thus improving the Sharpe ratio. The maximum drawdown is also significantly diminished.

The article quotes two merger arbitrage funds with substantial assets: The Merger Fund® (MERFX) and The Arbitrage Fund (ARBFX). To effectively diversify the balanced portfolio, should either fund replace a portion of stocks, a portion of bonds, or a combination of both? What should be the extent of such a replacement?

To answer the first question, let’s take a look at the correlation between SPY, AGG and either fund using the Correlation service of the Alpholio™ app. Here is a chart of the rolling 12-month correlation coefficient for monthly returns of SPY and MERFX:

Correlation SPY - MERFX

The starting date of the chart stems from the earliest availability of AGG whose first full monthly return was in October 2003. The average correlation of 0.56 indicates that MERFX was a marginal diversifier for SPY (generally, a correlation of 0.6 or less is desirable). Here is a similar chart for AGG and MERFX:

Correlation AGG - MERFX

The average correlation of just below zero indicates that MERFX was a much better diversifier for AGG than SPY. Similarly, the average correlation between SPY and ARBFX was about 0.42 and virtually zero between AGG and ARBFX. Therefore, to effectively diversify the base portfolio, it should generally be better to allocate more of SPY rather than AGG to MERFX or ARBFX. However, this would also suppress portfolio returns — as the following total return chart shows, MERFX and ARBFX had steadier but smaller cumulative returns than SPY:

Total Return of SPY, MERFX and ARBFX

To answer the second question: a portfolio with the highest Sharpe ratio (i.e. the tangency portfolio) would be mostly composed of AGG and MERFX. Here is an efficient frontier chart in which the current portfolio, depicted by a standalone marker inside the frontier, had 80% in AGG and 20% in MERFX but no SPY and was very close to the tangency portfolio:

Efficient Frontier 0% SPY + 80% AGG + 20% MERFX

Adding MERFX at the expense of SPY decreased the portfolio volatility and increased its Sharpe ratio, but resulted in lower returns. To illustrate this further, here is a chart and statistics for a portfolio that consisted of 45% SPY, 40% AGG and 15% MERFX, rebalanced quarterly:

Portfolio 45% SPY + 40% AGG + 15% MERFX

Ultimately, it is up to the investor to trade off portfolio returns for risk — some may choose to optimize for the highest return per unit of risk, while others may strive for higher returns at the expense of a sub-optimal Sharpe ratio. The Alpholio™ app for Android provides a set of tools that facilitate the exploration of historical data and construction of desired portfolios, with the usual caveat that the past performance is not a guarantee of future results.


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Timing of IRA Contributions
asset allocation, market, valuation

With the start of a new calendar year, many investors are considering making 2014 contributions to their individual retirement accounts (IRAs). However, given the recent appreciation of stocks to the perceived point of overvaluation, and poor prospects for bonds in light of an anticipated rise in interest rates, many investors may hesitate to make early contributions. This brings about two questions: What is the historical penalty for such procrastination? What happens if the investor decides to spread the annual contribution over time in the allowable period?

A simplistic answer to the first question is given in an article in The Wall Street Journal:

Contributing $5,500 to an individual retirement account each January, rather than in April of the following year, over 31 years (with an average annual 7% return) could boost the IRA balance by $55,000.

This calculation assumes a constant rate of return on investment in each year, which is unrealistic. In addition, it assumes that the contribution is fixed at a currently allowed maximum amount, even though in recent years the maximum has been revised upwards to approximate inflation (granted, historical maximum contribution was fixed at $2,000 between 1981 and 2001). Also, it does not specify the percentage increase of the terminal balance. Finally, it does not specify the exact nature of the “moderate” portfolio in the IRA.

To provide a more accurate answer to both questions, Alpholio™ conducted a mini study. (Since this post is longer than a usual one, time-pressed or impatient readers may want to skim the charts and navigate right to conclusions at the end of this write-up.)

The Study

To make study results tangible, instead of pure indices, two low-cost, no-transaction-fee investment vehicles with sufficiently long life spans were chosen: the Vanguard 500 Index Fund Investor Shares (VFINX) and Vanguard Total Bond Market Index Fund Investor Shares (VBMFX) mutual funds. The younger of the two, VBMFX, determined the longest feasible study period beginning in January 1987. For both funds, total (i.e. with reinvested distributions) rather than just price returns were used.

Various IRA portfolios, ranging from 100% stocks (all-VFINX), to 60% stocks and 40% bonds (the “standard” portfolio), to 100% bonds (all-VBMFX) were investigated. All portfolios were rebalanced monthly to their nominal asset allocations. Instead of a fixed contribution, a maximum contribution allowed by law in each historical year was assumed. The study did not take into account the higher “catch-up” contributions allowed for older investors, or any withdrawals or mandatory distributions that could trigger taxes or penalties.

The study considered two scenarios. In the lump-sum scenario, the maximum allowable contribution was made in whole at the beginning of a single month ranging from January of the contribution year to the following April (the deadline for making a contribution for the prior calendar year typically falls in mid-April). In the dollar-cost averaging (or “spread”) scenario, the contribution was evenly split and made at the beginning of a number of months starting in January of the contribution year.

The type of scenario determined the terminal year of investment. In the lump-sum scenario, the terminal investment could be made from January 2012 to April 2013 (that is because as of this writing, monthly data through April 2014 are not yet available). To roughly time-align with the lump-sum scenario, the spread investment scenario assumed that the terminal investment would take place in 2012.

For all asset allocations, the penalty was calculated as one minus the ratio of the terminal value of the portfolio with delayed or spread investments to the value of the portfolio when all investments were made as early as possible in January (baseline). For example, if delayed or spread investments resulted in a terminal portfolio value of $93,000 and January lump-sum investments generated $100,000, then the penalty was 1 – 93/100 = 7%.

The Lump-Sum Scenario

As could be expected, due to generally positive returns of stocks and bonds over time, a delayed lump-sum investment carried a penalty. Here is the penalty for a 100% stock and 0% bond (100/0) portfolio:

Lump Sum Penalty for 100 / 0 Portfolio

Generally, the lump-sum penalty had a positive relationship with the investment delay — the longer investor waited, the bigger the shortfall of the terminal value of the portfolio. However, the penalty did not always grow monotonically with the delay, as can be seen by its significant decrease in November and December in the above chart.

This particular case underscores the impact of first years of investing. Here, the almost 22% negative stock market return in October 1987, followed by a negative 8% return in November 1987, caused the penalty to diminish if the investor delayed the contribution toward the end of that year. To further illustrate the importance of early contributions in the IRA life cycle: The $2,000 invested in January 1987 was worth over $27,000, or about 10% of the terminal value portfolio, at the end of 2013.

The trend line in the chart shows that on average a procrastinating investor suffered a penalty of 0.66% of the terminal portfolio value per month of delay, culminating in about 12% of penalty if all investments were made in April of the year following the contribution year.

The more the IRA portfolio tilted towards bonds, the smaller the penalty. Here is a chart for a standard portfolio:

Lump Sum Penalty for 60 / 40 Portfolio

With this asset allocation, the penalty reached just over 10% and accrued at 0.63% per month.

For a 40% stock and 60% bond portfolio, the maximum penalty was just below 10% and grew at an average rate of 0.60% per month:

Lump Sum Penalty for 40 / 60 Portfolio

Finally, for a bond-only portfolio, the penalty peaked at just over 7.5% and increased by 0.52% per month on average:

Lump Sum Penalty for 0 / 100 Portfolio

According to the article:

An analysis of traditional and Roth IRA contributions made by Vanguard Group customers for the 2007 through 2012 tax years showed that, on average, 41% of the dollars contributed to IRAs for any given tax year are invested between January and April of the following year. Half of those dollars are contributed in the first half of April—the final weeks when contributions for the previous year can be made. The study found only 10% of dollars are contributed in January of the corresponding tax year, the earliest month contributions can be made.

This means that the majority of investors pay a significant price for delaying their investments. Granted, many investors may find it hard to come up with a lump sum for the entire contribution each January. Others may want to spread their investment over two or more months to minimize the risk in fluctuating market conditions. Let’s take a look at the effects of the latter scenario next.

The Spread Scenario

For a stock-only portfolio, uniformly dividing the annual contribution carried an average penalty of 0.53% per each additional spread month. When the contribution was dollar-cost averaged over the entire year, the total penalty was just over 5.5%:

Spread Penalty for 100 / 0 Portfolio

For a standard portfolio, the penalty accrued at 0.41% per additional spread month to reach almost 4.5%:

Spread Penalty for 60 / 40 Portfolio

For a more conservative 40% stock and 60% bond portfolio, the penalty increased on average by 0.34% per month and peaked at almost 4%:

Spread Penalty for 40 / 60 Portfolio

Finally, for a bond-only portfolio, the penalty rose by 0.22% per spread month to reach a maximum of just over 2.5%:

Spread Penalty for 0 / 100 Portfolio

The above findings are consistent with those of a Vanguard study on outcomes of lump-sum and dollar-cost averaging of investments. That study used fixed 10-year intervals, sliding by one month in a longer period of 1926 to 2011. It found out that for a standard portfolio, in 67% of cases a lump-sum investment outperformed dollar-cost averaging over the first 12 months of each 10-year interval. The terminal value of the lump-sum portfolio was on average 2.3% higher than that of the dollar-cost averaging portfolio.

Conclusions

Not surprisingly, delaying or spreading IRA contributions within the allowable 16-month window for each contribution year resulted in a penalty of a lower terminal value of the portfolio. The per-month average accrual rate and the magnitude of the penalty depended on asset allocation in the portfolio: The more tilt toward equities, the higher the rate and magnitude. Contributions in early years had a dominant impact on penalty distribution due to compounding of returns.

Clearly, investors pay a substantial price for procrastination in a lump-sum contribution scenario. Therefore, the investment for a given contribution year should generally be made as soon as possible. However, in many cases a full contribution amount may not be available early in the year, the investor may be averse to taking the risk of a lump-sum investment in given market conditions, or may not have a complete view of his/her income and tax situation until later in the contribution time frame. In that case, dollar-cost averaging with smaller sums can help lower the risk of a one-time investment and penalty for a delayed contribution.

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Asset Allocation in Retirement Portfolio
asset allocation, equity risk premium

A study by Pfau and Kitces in the Journal of Financial Planning gives a counter-intuitive guidance on asset allocation in a retirement portfolio. Instead of a traditional glide path that decreases the equity portion of the portfolio with the retiree’s age, the authors found that a rising allocation is optimal for retirement success, i.e. not running out of money.

The authors conducted 10,000 Monte Carlo simulations with three different sets of assumptions about stock and bond returns, equity risk premia as well as inflation rates, 121 lifetime asset allocation glide paths, annual withdrawal rates of 4% and 5%, and time horizons of 20, 30 and 40 years. The conclusions were:

Accordingly, for those households looking to maximize their level of sustainable retirement income, and/or to reduce the potential magnitude of any shortfalls in adverse scenarios, portfolios that start off in the vicinity of 20 percent to 40 percent in equities and rise to the level of 60 percent to 80 percent in equities generally perform better than static rebalanced portfolios or declining equity glide paths. The results hold even in situations where the final equity exposure is no higher than what the client’s static portfolio allocation may have been in the first place.

The results also reveal that in particular scenarios where the equity risk premium is depressed, the optimal glide path includes less equity overall. In scenarios where the goal is to withdraw at a level that stresses the portfolio [5%] and its expected growth rate, higher overall levels of equity are necessary (with such high-risk goals, having a relatively high-risk portfolio, even with the danger this approach entails, is still the optimal solution).

The key reason for starting with the initial lower allocation to stocks is that

…in the case of a 30-year time horizon, the outcome of a withdrawal scenario is dictated almost entirely by the real returns of the portfolio for the first 15 years. If the returns are good, the retiree is so far ahead relative to the original goal that a subsequent bear market in the second half of retirement has little impact. Although it is true that final wealth may be highly volatile in the end, the initial spending goal will not be threatened. By contrast, if the returns are bad in the first half of retirement, the portfolio is so stressed that the good returns that follow are absolutely crucial to carry the portfolio through to the end.

This is supported by Vanguard portfolio allocation models that range from 100% bond to 100% stock allocations and are analyzed in the 87 years from 1926 through 2012. As can be expected, the average annual return of a portfolio increases with allocation to equities, but generally so does the number of down years as well as the maximum annual loss. So, is there an optimal allocation that would maximize the average annual return while minimizing the probability of a loss year? To determine that, Alpholio™ compiled the following chart:

Average Return / Probability of Loss Year

The ratio peaks for a portfolio with 20% stocks and 80% bonds, which is consistent with the findings of the study.

The main problem with this and similar studies is that they assume a mechanical annual adjustment of withdrawals based on the prior year’s inflation rate. This is done to maintain the purchasing power of withdrawals. However, in reality expenses fall with age during retirement, as an article in The Wall Street Journal indicates:

“Pretty much every paper you read about retirement assumes that spending increases every year by [the rate of] inflation,” Mr. Blanchett says. But when he analyzed government retiree-spending data, he found otherwise: Between the ages of 65 and 90, spending decreased in inflation-adjusted terms.
Most models would assume that someone spending $50,000 the first year of retirement would need $51,500 the second year (if the inflation rate were 3%). But Mr. Blanchett found that the increase is closer to 1%, which has big implications over decades, “because these changes become cumulative over time,” he says.

In the above example, the terminal annual withdrawal after 25 years would be $104,689 with a 3% annual increase vs. only $64,122 with a 1% increase. This significant difference would certainly change the outcome of simulations with the rising equity glide paths. Most likely, either a flatter (less risky) path would suffice for a given success rate, or a success rate would increase for a given glide path.

To determine the optimal asset allocation in retirement, it is also useful to see the spending distribution among major expense categories:

Where the Money Goes

Not surprisingly, in a typical retirement period healthcare and charity expenditures grow, while insurance/pensions, transportation and clothing expenditures shrink as a percentage of the overall budget. A recent slowdown in medical-price inflation, which historically outpaced the overall inflation, is likely a result of passing on more costs to consumers (as well as a temporary effect of the Great Recession). Therefore, it seems reasonable to keep a sizable exposure to equities even late into retirement, while minimizing the risk in early years. This is what a U-shaped glide path strives to accomplish.

For most of current retirees, Social Security is a major source of income:

Keep It Coming

However, with the ongoing shift from the defined-benefit to defined-contribution plans, careful (and individualized) planning of retirement asset allocation in employer-sponsored plans and IRAs as well as other personal investments is evermore important.

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Rebalancing Act
asset allocation, foreign equity, market, mutual fund, valuation

As the end of the year approaches, the investment industry is gearing up for the annual portfolio rebalancing act. An article in InvestmentNews gives the following example:

Still, advisers’ plan to stick to their long-term asset allocation was likely thrown out of whack this year by the divergence of stocks and bonds. For example, a client who started the year with a simple 60/40 portfolio comprised of the $287 billion Vanguard Total Stock Market Fund (VTSMX) and the $247 billion Pimco Total Return Fund (PTTAX), the two largest mutual funds in the world, would now have 66.3% invested in stocks and just 33.7% invested in bonds, pushing beyond the typical 5% leeway most advisers give their asset allocation.

To illustrate the divergence from asset allocation historical averages, here is a chart from a Vanguard blog post:

Mutual Fund and ETF Assets under Management

While the collective allocation of mutual funds and ETFs to equities has recently reached 57%, the biggest divergence from the historical median is in international equities. Allocation to bonds is also relatively high, while the proportion in domestic equities is close to the 20-year median.

The higher allocations to international equities and bonds are at the expense of cash. Assets in money market funds are at a historical minimum of about 18% in the observation period. This has undoubtedly been caused by the low interest rate policy of the Fed, which depressed returns of such funds. The danger is that when interest rates eventually rise, bond prices will suffer:

So in an intermediate-term bond fund, with an average duration of four to five years, the loss would be about 4% to 5%.

This means that it may actually be prudent for an average investor to shorten the duration by moving a part of investment in bonds to money market funds.

Historically, the proportion of international equities in the total equity allocation has been about 19%; currently, it is about 27%. The argument for keeping it high is a relatively low valuation of foreign stocks compared to domestic ones:

Stock Valuation per Market Region

When rebalancing portfolios, it is also important that investors understand the true exposure of their mutual fund holdings to various asset classes. The recurring problem, which Alpholio™ addressed in several prior posts, is that managers in some equity funds (especially value strategies) hold a large percentage of assets in cash. As a result, asset allocation in the overall portfolio can be distorted unbeknownst to the investor.

Alpholio™ provides current information on the exposure of mutual funds to various asset classes. This information is not obtained from the regulatory filings or selective disclosures of fund holdings, which suffer from a number of problems.

In sum, when rebalancing a portfolio either on a fixed schedule or as a result of divergence from prior allocations, investors should take into account a broader market and interest rate context, rather than just follow rigid rules.

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Under the Hood of Tactical Allocation Funds
analysis, asset allocation, mutual fund

An article from The Wall Street Journal describes a new wave of “tactical allocation” mutual funds:

There are 41 mutual funds with “tactical” in their names that are tracked by investment-research firm Morningstar Inc., including 18 that were launched since the beginning of 2012. Total assets in this fund category have risen to $4.92 billion from $1.10 billion in December 2007, according to Morningstar.

Successors to the so-called market-timing funds of the past, tactical allocation funds attempt to shift between asset classes

…with the idea of exploiting the stock market’s strong points and dodging its weaker corners over time.

One of such funds mentioned in the article is Leuthold Core Investment Fund (LCORX):

Douglas Ramsey, one of the managers of the Leuthold Core Investment Fund, says the fund’s goal is to match the performance of the stock market over the full cycle with substantially less risk, which it has done.

The fund can shift its stock exposure from 30% to 70%, and now holds 60%, Mr. Ramsey says. While it was originally conceived as a core portfolio holding, it’s now often used by registered investment advisers as a part of their alternatives allocation, Mr. Ramsey says.

Let’s take a look at the fund’s performance from the Alpholio™ perspective. The cumulative RealAlpha™ chart shows that the fund did not add value on a truly risk-adjusted basis, i.e. vs. a dynamic reference portfolio of exchange-traded products (ETPs):

Cumulative RealAlpha™ for LCORX

The fund’s statistics demonstrate that despite a low TrueBeta™, the volatility of the fund’s returns was higher than that of the reference portfolio, and the annualized RealAlpha™ was negative:

LCORX Statistics

The reference weights chart depicts how the fund’s asset allocation changed over time:

Reference Weights for LCORX

An equivalent fixed-income position of the fund is represented by the iShares 1-3 Year Treasury Bond ETF (SHY). In 2008, this position was insufficient to cushion equity declines and, as a result, the fund returned about -27.4%. From mid-2009 to mid-2010, in an attempt to capitalize on the stock market’s rebound, the fund started to decrease this position. However, the decrease was too gradual and ultimately reversed in the second half of 2010. Consequently, in 2010 the fund returned only 3.5% compared to about 12% of its peers. This illustrates the difficulties tactical allocation managers have with market timing.


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How Much to Invest Abroad
asset allocation, correlation, foreign equity, portfolio

A recent article in the Wealth Management Report of The Wall Street Journal provides recommendations from industry experts on what portion of the portfolio an individual investor should invest in foreign securities. The expert opinions focus on equity, rather than bond or currency, allocation in the portfolio. Although the sample of just seven experts is small, statistics show that opinions do not vary a lot:

Statistic Value
Mean 27.5%
Median 30.0%
Standard Deviation 6.9%

So, is a foreign equity allocation in the high 20s percent points appropriate? It depends on whether this brings the benefit of high and uncorrelated returns to the rest of the portfolio. In his bestselling book, David Swensen recommends the following asset allocation as the starting point for individual customization:

Asset Class Policy Target
Domestic Equity 30%
Foreign Developed Equity 15%
Emerging Market Equity 5%
Real Estate 20%
U.S. Treasury Bonds 15%
U.S. Treasury Inflation-Protected Securities 15%

This implies an explicit foreign equity exposure of 20% of the total portfolio and about 28.6% of its equity portion (20% in a portfolio with 70% of “assets that promise equity-like returns”). Swensen also discusses currency exposure that stems from foreign investments:

“Fortunately, finance theorists conclude that some measure of foreign exchange exposure adds to portfolio diversification. Unless foreign currency positions constitute more than roughly one-quarter of portfolio assets, currency exposure serves to reduce the overall portfolio risk. Beyond a quarter of portfolio assets, the currency exposure constitutes a source of unwanted risk.”

Unfortunately, the diversification provided by foreign equities tends to fail when it is needed most. Since the most recent financial crisis, correlations between foreign and domestic equity returns shot up. Vanguard reports that from October 2007 through February 2009, that correlation was 0.93 for developed international markets and about 0.83 for emerging markets.

At the same time, even a domestic equity portfolio has an implicit exposure to foreign markets. That is because about 46% of revenue of companies in the S&P 500® index has been historically obtained abroad. In sum, an explicit allocation of close to 30% of the equity portfolio to foreign securities, which on average experts recommended, may be on the high side.

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