1.3.1 The Volatility of the Financial Market

The dynamics and volatility of the financial market is well known.

For example, consider the Chicago Board of Options Exchange (CBOE) index:

CBOE Volatility Index®: Chicago Board Options Exchange index (symbol: VIX®) is the index that shows the market's expectation of 30-day volatility. It is constructed using the implied volatilities of a wide range of S&P 500 index options. This volatility is meant to be forward looking, is calculated from both calls and puts, and is a widely used measure of market risk, often referred to as the “investor fear gauge.”

The VIX volatility methodology is the property of CBOE, which is not affiliated with Janus.

Clearly, Figure 1.2 reflects the dynamic nature of a typical stock market over the past 20 years. One wonders if a rational financial engineering approach may be developed to sustain the two objectives at hand simultaneously:

1. To maintain a steady level of investment
2. To produce a steady income for the investors

The remainder of this book will provide rational approaches to achieve these joint goals.

1.3.2 Ongoing Results of the XYZ–LPL Investment of the Account of Mr. and Mrs. Smith

Let us first examine the results of this investment opportunity, as seen over the past 10 years approximately.

Investment Results of the XYZ–LPL (Linsco (1968) and Private Ledger (1973)) is illustrated as follows:

LPL Financial Holdings (commonly referred to as LPL Financial) is the largest independent broker-dealer in the United States. The company has more than 14,000 financial advisors, over $500 billion in advisory and brokerage assets, and generated approximately $4.3 billion in annual revenue for the 2015 fiscal year. LPL Financial was formed in 1989 through the merger of two brokerage firms – Linsco (established in 1968) and Private Ledger (established in 1973) – and has since expanded its number of independent financial advisors both organically and through acquisitions. LPL Financial has main offices in Boston, Charlotte, and San Diego. Approximately 3500 employees support financial institutions, advisors, and technology, custody, and clearing service subscribers with enabling technology, comprehensive clearing and compliance services, practice management programs and training, and independent research.

LPL Financial advisors help clients with a number of financial services, including equities, bonds, mutual funds, annuities, insurance, and fee-based programs. LPL Financial does not develop its own investment products, enabling the firm's investment professionals to offer financial advice free from broker/dealer-inspired conflicts of interest.

1. Revenue: US$4.37 billion (2014)
2. Headquarters: 75 State Street, Boston, MA, USA
3. Traded as: NASDAQ: LPLA (https://en.wikipedia.org/wiki/LPL_Financial)

Over the past 10 years, the Smiths' received, on a monthly basis, a net income of $10,947.03. Thus, annually, the income has been

And, the total income for the past 10 years has been

Illustrated hereunder in Figure 1.3 is a snapshot of one of the four investment accounts of the Smiths'. Note the following special features of this portfolio:

1. The green area represents the investment amount: As portions of the capital were being periodically withdrawn (to satisfy U.S.A. Federal Regulations), the actual investment amount decreases in time. This loss has been more than made up by the blue area!
2. The blue area is the portfolio value of the account.

This showed that, as steady income is being generated, the portfolio value grows more than the amounts continually withdrawn – periodically and regularly.

Clearly, the goals of the investment have been achieved!

While the exact algorithms used by XYZ/LPL is proprietary, the following investment strategies are clear:

1. Have each investment account placed in high-yield corporate bonds, and then SET a maximum limit of 3% draw down (loss) limit for each investment account.
2. If draw down > limit of 3%, then move investment account over to cash or money market accounts – to preserve the overall capital of the portfolio.
3. Stay in the cash or money market accounts, until the following three conditions of the market become available before returning to the high-yield corporate bonds where opportunity becomes available once again:
   1. Favorable conditions have returned – when comparing high-yield corporate bonds and the interest rates of 10-year Treasury notes, namely, when condition favoring the relative interest rates of money.
   2. Favorable conditions have returned – when comparing the volumes of money entering and leaving the market, namely, whether investors are “Pulling Back.”
   3. When the direction of the market becomes clear.

It certain does not escape ones attentions that these set of conditions are rather tenuous, at best.

One should, therefore, seek more robust paths to follow.

1.4.1 Modern Portfolio Theory (MPT)

In MPT, it is assumed that investors are risk averse, namely, if there exist two portfolios that offer the same expected return, rational investors will prefer the less risky one. Thus, an investor will accept increased risk only if compensated by higher expected returns. Conversely, an investor who wants higher expected returns must accept more risk. That is,

(1.1)

1.4.2 Asset Allocation and Portfolio Volatility

It is reasonable to assume that a rational investor will not invest in a portfolio if there exists another available portfolio with a more favorable profile. Portfolio return is the proportion-weighted combination of the constituent assets' returns.

1.4.3 Characteristic Properties of Mean-Variance Optimization (MVO)

The following are the characteristic properties of the methodology of MVO:

1. It does not take into account “fat-tailed” asset class return distributions, which matches mast real-world historical asset class returns. For example, consider the monthly total returns of the S&P 500 Index, dating back to 1926: There are 1,025 months between January 1926 and May 2011. The monthly arithmetic mean and standard deviation of the S&P 500 Index over this time period are 0.943 and 5.528%, respectively. For a normal distribution, the return that is three standard deviations away from the mean is −15.64%, calculated as (0.943%–3 × 5.528%).

   In a standard normal distribution, 68.27% of the data values are within one standard deviation from the mean, 95.45% within two standard deviations, and 99.73% within three standard deviations: Figure 1.4

   This implies that there is a 0.13% probability that returns would be three standard deviations below the mean, where 0.13% is calculated as

   

   In other words, the normal distribution estimates that there is a 0.13% probability of returning less than −15.64%, which means that only 1.3 months out of those 1,025 months between January 1926 and May 2011 are expected to have returns below −15.64%, where 1.3 months is arrived at by multiplying the 0.13% probability by 1,025 months of return data.

   However, when examining historical data during this period, there are 10 months where this occurs, which is

   

   or almost 8 times more than the model prediction!

   The following are the 10 months in question:

   Month	Return (%)
   Jun 1930	−16.25
   Oct 2008	−16.79
   Feb 1933	−17.72
   Oct 1929	−19.73
   Apr 1932	−19.97
   Oct 1987	−21.54
   May 1932	−21.96
   May 1940	−22.89
   Mar 1938	−24.87
   Sep 1931	−29.73

   The normal distribution model also assumes a symmetric bell-shaped curve, and this seems to imply that the model is not well suited for asset classes with asymmetric return distributions. The histogram of the data, shown in Figure 1.5, plots the number of historical returns that occurred in the return range of each bar.

   The curve plotted over the histogram graph shows the probability predicted by the normal distribution. In Figure 1.5, the left tail of the histogram is longer, and there are actual historical returns that the normal distribution does not predict.

   Xiong and Idzorek showed that skewness (asymmetry) and excess kurtosis (larger than normal tails) in a return distribution may have a significant impact on the optimal allocations in a portfolio selection model where a downside risk measure, such as Conditional Value at Risk (CVaR), may be used as the risk parameter. Intuitively, besides lower standard deviation, investors should prefer assets with positive skewness and low kurtosis. By ignoring skewness and kurtosis, investors who rely on MVO alone may be creating portfolios that are riskier than they may realize.

2. The traditional MVO assumes that covariation of the returns on different asset classes is linear. That is, the relationship between the asset classes is consistent across the entire range of returns. However, the degree of covariation among equity markets tends to go up during global financial crises. Furthermore, a linear model may well be an inadequate representation of covariation when the relationship between two asset classes is based at least in part on optionality such as the relationship between stocks and convertible bonds. Fortunately, nonlinear covariation may be modeled using a scenario- or simulation-based approach.
3. The traditional MVO framework is limited by its ability to only optimize asset mixes for one risk metric, standard deviation. As already indicated, using standard deviation as the risk measure ignores skewness and kurtosis in return distributions. Alternative optimization models that incorporate downside risk measures may have a significant impact on optimal asset allocations.
4. The traditional MVO is a single-period optimization model that uses the arithmetic expected mean return as the measure of reward. An alternative is to use expected geometric mean return. If returns were constant, geometric mean would equal arithmetic mean. When returns vary, geometric mean is lower than arithmetic mean. Moreover, while the expected arithmetic mean is the forecasted result for the next one period, the expected geometric mean forecasts the long-term rate of return. Hence, for investors who regularly rebalance their portfolios to a given asset mix over a long period of time, the expected geometric mean is the relevant measure of reward when selecting the asset mix.

   

   

In spite of its limitations, the normal distribution has many attractive properties:

It is easy to work within a mathematical framework, as its formulas are simple.

The normal distribution is very intuitive, as 68.27% of the data values are within one standard deviation on either side of the mean, 95.45% within two standard deviations, and 99.73% within three standard deviations, and so on.

1.5.1 Examples of Modeling Asset Classes

1.8.1 Day Trading

Day trading is the speculation in stocks, bonds, options, currencies, and future contracts and other securities, by buying and selling financial instruments within the same trading day. Once, day trading was an activity exclusive to professional speculators and financial companies. The common use of “buying on margin” (using borrowed funds) greatly increases gains and losses, such that substantial gains or losses may occur in a very short period of time.

1.8.2 Algorithmic Trading

Algorithmic trading is a method of placing a large order by sending small portions of the order out to the market over time. It is an automated method of executing an order using automated preprogrammed trading instructions providing preset instructions accounting for variables such as price, volume, and time. It claims to be a way to minimize the costs, market impacts, and risks in the execution of an order – thus eliminating human intervention and decisions in the process.