Tuesday, March 27, 2012

Best Practices for Asset Allocation

This article from CNN.com lists 14 best practices for asset allocation.

The List
1. Time is on your side.
Well it is until it isn't I guess
2. Stocks mean risk and return.
3. Get professional advice!
Especially if time isn't on your side.
4.Allocation is key to achieving your goals.
5.Know your stock funds.
6.Know your bond funds.
7. Don't rely on software alone to build your portfolio
8. College savings funds need stocks.
9. Determine your long term goals
10. Get Started!
Time is running out!
The rest of the article is a statement of the obvious. Like this

"Your risk tolerance and goals will determine how much you put into each of the three investment categories. If you make careful choices with your asset allocation, you'll earn better returns without losing sleep."

The article ends in agreement with the book-asset allocation involves jusgement so no 2 perfect solutions will be the same.

Asset Allocation and Risk Management in Bimodal World



  • ​Fat tails and negative skewness in the distribution curve can arise from the mere possibility of multiple equilibria – even if both equilibria individually appear normal.
  • Once markets arrive at a resting place among different equilibria, they tend to become trapped due to a variety of restraining forces.
  • For all these reasons, we believe that the core building blocks of asset allocation and option pricing in the current macroeconomic environment should allow for the possibility of multimodality. This significantly changes the conceptual approach towards portfolio construction and risk management.


The article introduces the concept of "Bimodal Distribution."  Market participants  relied on a modeling framework that considered a single "equilibrium". But a key impact of the recent bout of crises hitting global markets has been the possibility of the emergence of multiple equilibria, which might happen if one or another competing force takes the upper hand.

The bimodal distribution has two peaks, and interestingly, even though it is generated as the result of mixing two normal distributions, each from a different regime, it can exhibit both fat tails (a higher probability of larger losses due to unusual events results in a “fat tail” on the left side of the distribution curve) and skewness (a lack of symmetry between the left and right sides of the peak).

The application on "Bimodal"

Optimal Allocation to Risky Assets: If we start with an assumption that we would allocate 50% of the portfolio to equities in the unimodal case, what would the optimal allocation be in the bimodal case, assuming our risk preferences are unchanged? By following a very traditional portfolio optimization exercise which involves a little bit of math, the answer turns out to be that the optimal allocation would be only 10%! In other words, one would have to de-risk by almost 80% from the current optimal allocation to arrive at the mathematically optimal result. The prospect of being trapped in a low return, low probability event requires us to, as Mohamed El-Erian would say, “generally play defense and selectively play offense.”

Pricing of Options on Tails: If we started with an assumption of unimodality and the real distribution turned out to be the bimodal one, how mispriced would put options on the tails be in retrospect? Our research shows that a typical unimodal distribution just cannot be tweaked large enough to make it come out with the price of a put option one would likely get if the real world turned out to be bimodal. A portfolio manager pricing such tail options armed with traditional unimodal distributions would wrongly think that the tail options were “expensive” (tail options will generally tend to be underpriced when based on a unimodal distribution but significantly higher when derived from bimodal distributions).


Fat tails and negative skewness can arise from even the mere possibility of multiple equilibria, even though both equilibria in themselves are normal. This practice of generating very complex distributions from mixtures of simple, normal distributions is well known among statisticians and has applications in many fields of practical import: medicine, astronomy and casino gambling to name a few. 



Monday, March 26, 2012

Owning Apple Stock Could be a Double-Edged Sword

For this week's post, I found a short, but interesting article from Reuters (via Yahoo! Finance, found here) about the pluses and minuses of funds' recent overload of Apple stock in their portfolios. According to Morningstar, as of right now, 46 funds have Apple stakes greater than 9%, which is more than double their weighting in the S&P 500 index.

Many mutual funds are now facing a dilemma with regards to their holdings of Apple. On the one hand, returns have been well above benchmarks due to outstanding holding period returns since the Apple stock was purchased. On the other hand, however, these funds now face increased risk due to much larger portions of their portfolios invested in just Apple, sometimes upwards of more than 10%. So what was originally a great strategy has now exposed these funds to major risk in the case that Apple's fortunes change.

The dilemma is whether or not these funds are willing to sacrifice potential future returns in order to reduce their proportion of Apple and reallocate the risks. The outlook for Apple is generally positive, but one bit of bad news could have these funds reeling if they choose to keep their proportions of Apple as high as they are currently. Selling off their positions could prove to be an unpopular move, however, as Apple has gained 48% in 2012 alone.


Sunday, March 25, 2012

The CAPM Model

Throughout most of our finance classes we have learned about the CAPM Model which we used to determine the appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. This model used Beta as its measure of sensitivity to the non-diversifiable risk. This week I came across an article which talked about the deficiencies of the CAPM Model and criticized the used of Beta for a measure of risk. The article states that Beta measures the sensitivity of an asset to an index and that this is only useful if you care about relative performance. Relative performance may not be the best way to judge an asset since it doesn't matter if you are beating the market by 2% if the market is down by 20%. The author also criticizes two of the assumptions of the CAPM model. First, the CAPM model is based on the assumptions that investors are rational and the author goes on to say that especially in money matter investors tend to get emotional. Secondly, the CAPM Model is based on the assumption that all information is available at all times to investors. While this may be true, especially with the Internet, even if all the information was available most investors wouldn't know what to do with it. The author thinks that the reason Beta is still important is because just like standard deviation or other measures, Beta is a measure based on numbers and people tend to find comfort in numbers. However, he believes that risk cannot be
entirely quantified and that there is a need for business sense and skeptical thinking when investing.

http://www.tradingfloor.com/posts/why-capm-is-useless-1583337652

Tuesday, March 20, 2012

A Few Takes on Diversification

This week I decided to take a look at a few articles dedicated to different approaches to diversification.

The first article, called "The Right Kind of Diversification" (found here), talks about how there are actually two different reasons that investors diversify. The first is the traditional reason: to protect against losses in one asset class by offsetting them with gains from another asset class. The second is a newer way to look at diversification: investors are worried about missing out on the next big upward trend in the economy, so they end up overloading their portfolios with as many different types of investments as they can. This second type of diversification is much more aggressive and competitive than the more conservative and traditional way of looking at it.

The author goes on to say that this kind of aggressive approach to diversification is unnecessary and can be "self-defeating". The desired level of diversification can be achieved by only owning a few funds rather than many. Furthermore, it makes little sense to load up on a variety of one asset class (e.g. ETFs) simply in the hope that one of them doubles or triples over the next few years. In other words, it is important to view diversification as a long-term strategy rather than a contest where the winner realizes the best returns, similar to winning the lottery.

In the next article, titled "The Error-Proof Portfolio: Take Diversification to the Next Level" (here), the author discusses ways to diversity more broadly beyond the simple portfolio construction approach.

1) Time Diversification: diversifying your purchases over several time periods helps to protect against various outcomes of the performance of the asset and interest rate fluctuations.

2) Tax Diversification: most investors/savers have their money in traditional IRAs or 401(k)s where withdrawals are taxed; the author suggests investing in a Roth IRA (or similar account) where future withdrawals are tax-free.

3) Vehicle Diversification: the author gives a few examples of how to improve the risk/reward profile of a portfolio--adding a passively managed index fund to a portfolio dominated by actively managed funds, or vice versa; and supplementing individual stock picks with a diversified mutual fund or ETF.

4) "All-In" Diversification: when thinking about diversification, consider putting your money into more liquid assets to offset your ownership in real estate or your business; also, consider your "human capital"--an employee with a safer, more steady income stream can afford to invest in assets with a higher volatility, while employees whose earnings are based on commissions, etc should invest in safer assets.

Monday, March 19, 2012

Concentrated Portfolios

This article from seekingalpha, shows the benefits of a concentrated portfolio strategy. The author states that his typical portfolio is made up of between 2o and 25 stocks. This:
"creates a little bit of additional volatility, but it also increases the odds that a strong performer will have an outsized positive impact on the account."
Willholding so few stocks increase volatility?
Not according to C. Thomas Howard who claims that with 20 stocks 90% of the market standard deviation is eliminated.

"Instead of limiting themselves to their 10 or so best ideas, the typical active equity mutual fund manager holds 100 stocks. As shown in Figure 2, the “last”-ranked stock earns a negative excess return of between -2% and -3%. In fact, excess returns go negative somewhere around 30th-best stock. Thus, the typical portfolio is comprised of 30 positive excess-return stocks and 70 negative excess-return stocks. Not exactly a recipe for success!"

So why don't funds limit themselves to their best picks?
  1. Funds earn fees based on assets under management-The bigger they are the better the managers do
  2. The need to track an index
  3. Investors fears about volatility

If I was a fund manager certainly the draw of higher fees would certainly influence me. But knowing that a 20-25 stock portfolio will do better than a 100 stock portfolio how can you turn your back on excess returns? Well I would be concerned that I would pick the wrong 20-25 stocks and lose my shirt, but I'm not a professional. So I'll probably stick with TIPS and I series bonds and leave my stock picking to contests.

The article ends with a great line,

"As always, the road to better returns is usually psychologically uncomfortable!"