How to lose the most money in 100 days
Breaking the rules of risk management to build a high-risk, low-yielding portfolio of financial stocks that will lose the most of a $100,000 investment
What is meant by risk? Risk is the chance that a return from an investment will differ from what is expected (What does risk mean?, 2009), so in terms of financial stocks risk is the chance of the return on an initial investment of stocks being different from the expected value of the investment at the end of the period of investment. To understand the idea further risk can be categorised into systematic (non-diversifiable risk) and non-systematic risk (diversifiable risk) (Different Types of Risk, 2008). Systematic risk will affect a large number of financial stocks that may be affected by a large political or economic event and is difficult to protect an investment against, whereas non-systematic risk may be specific to a company or group of companies belonging to a specific industry for example. It is the non-systematic risk that is of interest to investors who seek to reduce and manage this by constructing a diversified portfolio of shares, providing a sufficient return at an acceptable level of risk.
To be able to lose the most of an initial $100,000* investment in 100 days the opposite approach needs to be undertaken; identifying high-risk, low-yielding stocks from which a portfolio can be constructed in such a way that this non-systematic risk is kept as high as possible whilst having a sufficiently low portfolio return. Getting to this point involves a selection of qualitative and quantitative risk analysis methods to identify the constituent stocks of this portfolio from the many thousands of possible financial stocks available purchase.
Stocks to Consider
With the liquidity problems in the financial sector and the economic downturn now seen as a recession in both the UK and US (UK in recession as economy slides, 2009) many stock prices are likely to fall further and is having a significant effect on a number of companies. Housing and retailing are identified as areas identified as two areas in which the economy is most vulnerable to this downturn (Britain's sinking economy, 2008) with the housing market being affected by the more strict availability of mortgage finance, which in turn is resulting in a fall in house prices. Obviously this will have an effect on house-building companies and companies closely related to this industry who make profit in the process of buying, building and selling houses and buildings and therefore the risk of their associated stocks and price.
Retailing companies in the UK and US have been experiencing their lowest growth in sales for three years in the third quarter of 2008 (Pimlott, 2008), but cannot be said to be the general picture for all retailers. The author determines using data from the Office of National Statistics that food retailers experienced a boost in sales in this same period along with the continued growth of internet shopping. Non-specialised shops such as department stores have seen growth in sales fall by the largest recorded amount in the same period, affecting their ability to make money therefore can be seen as possibly high-risk stocks. Interestingly the collapse of the major retailer, Woolworths, described as non-specialised and one of the hardest hit in the previous article illustrates the increasing pressure now and in future on these types of companies and the increase in the non-systematic risk of their stocks (Hard sell, hard times, 2008).
The American car industry is another area of interest with car manufacturers struggling (US car giants report large losses , 2008) with the likes of General Motors and Ford reporting multi-billion dollar operating losses causing stock prices to plummet, due to a dramatic fall in demand for cars.
The initial list for consideration in the portfolio consists of a number of companies in the areas or related to the areas already mentioned and includes: Bellway, Bovis, Barratt and Redrow; some of the UK’s biggest house builders as well as Rightmove, a property advertising website with the majority of it's business dependant on this market. Some retailers from the US and UK are included: such as Debenhams one of the UK’s biggest department stores, Laura Ashley and other non-specialised retailers. A number of car manufacturers and dependants such as Johnson Controls, who conduct the majority of their business with manufacturers, are also selected. Chemicals companies such as DOW and JMAT have been included as the lack of demand in consumer goods and construction may have a knock-on effect of the demand of their products. Finally the stock of Phorm, an internet advertising company is included because of the ethical and legal debate surrounding its past and present operations (Fears over advert system privacy, 2008) providing potential high, specific risk to this company's stock.
These initial 25 stocks were used as part of an initial, preliminary analysis using financial ratios that indicate business risk and as a result the first five stocks considered to be of the lowest risk were discarded (AAPL, JCP, TM, DOW, JMAT.L).
Appendix A lists the stocks considered from this qualitative analysis.
Risk of a single stock
A reasonable estimation of the risk of a single stock can be determined from historical pricing data, which can be used to calculate the returns for a given period of time using the equation: Period Return = (Current period stock value – Previous period stock value)/Previous period stock value; with the period ranging from a day to a number of years. For a single stock, historical pricing data from the previous two years, showing the daily price is downloaded into an Excel spreadsheet from Yahoo Finance and the daily returns calculated using the return equation, in this case the period is a single day. The mean of this data or average return can be said to be the expected level of return from this stock over a single day, based on it’s historical performance. The risk of the stock is determined by the standard deviation of it’s historical returns as this measures the “spread” of the data about the mean. The higher this value the more risk a stock can be considered to have and can be calculated for each individual stock considered for the portfolio. When comparing stocks the variance is used; this is the square of the standard deviation.
Of particular notice are the variances for Land of Leather, Volkswagen and Phorm each of which is amongst the highest three variance values. The high variance of Volkswagen may be explained by a dramatic rise of 348% in the value of the shares over two days, subsequently falling 45% thereafter (Hedge funds make £18bn loss on VW, 2008). One off events such as these must be considered in addition to the historical data as they may have the effect of inflating the risk and could be considered a disadvantage of this type of analysis. Phorm has high variance because it is involved in transactions that do not occur often, but when they occur they inflict massive percent jumps in the value of the stock this may also be related to the nature and controversy of the company as already highlighted. Land of Leather stock value has fallen from approximately 300 to 9.
On the other hand the low variance stocks need to be highlighted in addition as these are considered lower risk stocks, which can possibly be discarded narrowing the portfolio stock selection. The lowest variance of the selection is 0.00642 belonging to LII.L as well as others RMV.L, JCI, BRBY.L and CPR.L. These stocks can possibly not be considered for the final portfolio because of their low risk, but before this decision is made another statistical analysis can be implemented to help make this decision in assessing risk.
Figure 1
Value at risk of a single stock
This is another risk analysis method of single stocks which can be implemented to help determine the shares considered for the portfolio. The result of this analysis produces the possible maximum loss on any given day of an initial investment with a level of confidence produced from historical price data for individual stocks. Again, the daily pricing information for the previous year up to 1 December of the various stocks under consideration was downloaded into Excel from Yahoo Finance and the daily returns calculated. The value at risk is calculated using two methods, the first being the historical method and the second the parametric method. Calculating the historical value at risk involves ordering the returns by magnitude from smallest to largest and finding the cumulative frequencies and their associated values of the confidence level desired by an investor completely based on the historical model of the stock. Alternatively the parametric method can be used assuming the behaviour of the rises and falls in stock value is that of a normal probability distribution function (PDF) based around the average daily return of the stock. The PDF can then be used to find the standard deviation at different percentage confidence levels, where each represents this percentage of the lowest return values. Either method can be used, each having their own advantages and disadvantages; the assumption is made when using the parametric method that the behaviour of the stock prices day-to-day follows the normal PDF behaviour. On the other hand the parametric method allows the value at risk for longer periods to be determined, whereas the historical method is confined to the historical data used.
The value at risk has been determined for all of the shares under consideration at a confidence level of 5% with an investment of 1000. Both the historical and parametric methods have been used at this confidence level. A graph showing the results of these methods can be seen in figure 2.
The higher the value at risk of a single stock, then the more risk the stock has because there is a 5% chance that a larger portion of the initial investment will be lost. Higher values at higher confidence levels indicate more risky stocks.
The results of this analysis identify the stocks with the lowest value at risk to be identical to those identified in the risk of a single stock analysis with LII.L having the lowest value at risk worked out using the historical method. It can be said that the most that could be lost in a single day would be 47.99 with 95% confidence and of course a 5% chance that the stock could lose more than this. RMV.L, CPR.L, JCI and BRBY.L have 61.82, 56.13, 56.77 and 61.7 values at risk respectively using the historical method and these can be seen to have the lowest values in figure 2. This means that these stocks can be discarded from consideration for the portfolio leaving 15 stocks to consider.
The Volkswagen stock again is immediately noticeable as having one of the highest values at risk due to its parametric analysis, with a value of 185.31 compared to the value of 52.30 for the historical analysis and shows the importance of considering both methods. Clearly this effect is due to the extreme rise and fall of the share price in a matter of days as described earlier. It cannot be certain that an event like this would happen again to this stock in the future and is probably extremely unlikely and because of this the historic value of risk is interpreted, which is low and so this company can also be discarded.
Companies with high values at risk will be considered for the portfolio and by examining figure 2 the stocks with the highest value at risk can be found. These are
AMD, GM, LAN.L, DSGi.L, DEB.L, JJB.L, BDEV.L, BVS.L, PHRX.L and ALY.L.
Figure 2 - Comparison of Value at Risk between stocks at 5% confidence
Building a portfolio
In order to begin to build a portfolio the relationship between the historical returns of different stocks need to be analysed together, previous analyses have concentrated on single stock analysis and then comparing the results.
The degree to which the returns on two shares vary in relation to each other can be found statistically by finding their covariance; an important issue to consider as it is this value which is used in portfolio diversification. Practically the correlation coefficient, a derivation of covariance is used because of it being confined to values between +/- 1 and is independent of the magnitude of change. A correlation of 1 between two stocks will ensure they move in same direction to the same degree at the same time and -1 in opposite directions. The significance of this is key to understanding portfolio theory and it’s use to manage risk.
Adding stocks with varying and opposing correlations will diversify a portfolio such that the diversifiable risk is reduced overall because the stocks will gain and lose to different magnitudes with some stocks gaining, whilst others lose their value. As more stocks are added with differing correlations, the diversifiable risk falls exponentially. Therefore, portfolio diversification needs to be ignored, with all shares in the portfolio having as high correlations as possible so that they are all subject to the same non-systematic risk. It is difficult to eliminate diversification altogether because stocks seldom have a perfect correlation and with a minimum of 5 stocks required this will happen. Ideally the investment would be in a single bad performing stock.
Correlations of the daily returns of the remaining stocks can be seen in figure 3, generated using the correlation data analysis tool in Excel.
Figure 3
Interestingly, the matrix contains a correlation value of approximately 0.68 between BDEV.L and BVS.L, the two house building companies and arguably could be considered predictable as they may both be subject to the same unsystematic, diversifiable risk. They both have a correlation with DEB.L of 0.4. The correlations between AMD, F and GM are also 0.4, 0.51 and 0.71 respectively, again high correlation values resulting in high risk but the correlation with the other stocks in the matrix is low.
The high correlation between BDEV.L and BVS.L led to the inclusion and analysis of a third house building company, BWY.L that was discarded earlier with the expectation that it too, will have a high correlation with the two other stocks. BWY.L is seen to have high correlations with BVS.L and BDEV.L at 0.71 and 0.82 respectively. This stock did not have one of the highest Values at Risk or standard deviation, but a trade-off can be made between these and the high correlations and by including it the risk of the portfolio is much higher. BDEV.L, BWY.L, BVS.L and GM are chosen as the portfolio stocks as these produce high correlations.
There are many different portfolios that can be constructed from these stocks, with each portfolio assigning different weightings to each of the stock investments resulting in different standard deviations (risk) and expected returns. The desired portfolio weightings are those that produce the highest standard deviation and sufficiently low return. Using the daily historical data and returns for each stock from the past year up to 1 December all possible stock investment weightings and therefore portfolios were determined, with a minimum weight of 10% and 60% as the minimum and maximum possible stock investment weights respectively. Produced in excel, this results in 125 different possible portfolios and the expected return, standard deviation and variance were calculated for each of them. Expected return can be calculated by summing the weighted averages of the returns of the stocks in the portfolio and the standard deviation by expanding the portfolio standard deviation equation for 5 stocks (more about this in Appendix B).
Figure 4
Figure 4 shows the daily risk/return plots for all possible portfolios containing these 5 stocks and is interesting to note that the left-hand side of the plots form an Efficient Frontier (Efficient Frontier, 2009); the resulting optimal portfolios and investment weights with the most efficient investment at the peak of the curve. Other plots underneath this curve are of interest as these represent higher-risk, inefficient portfolios with the same level of return as one of the possible optimal portfolios found on the frontier. This illustrates another risk analysis method, as an investor may use a graph such as this to identify a portfolio that provides a sufficient desired return for an acceptable level of risk. It also importantly indicates the lowest risk portfolio and the level of expected return.
So which is the portfolio required? This can be identified in figure 5 as the plot with the lowest expected return and highest risk/standard deviation and is the plot at the very bottom right of the graph with expected daily return and standard deviation of approximately -0.00469 and 0.0579 respectively and hence this portfolio is selected as the high-risk, low-yielding required.
The resulting portfolio has an uneven investment weighting with BDEV.L having 60% of the investment and the rest 10% minimum value. Considering the idea of diversification, correlations and single stock risks this is what is expected of the portfolio. BDEV.L has amongst some of the largest correlations with BVS.L and BWY.L, but not the highest which is 0.821 between BVS.L and BWY.L. Single stock and value at risk analysis demonstrated that BDEV.L had a larger variance and value at risk then the other stocks in the portfolio. Naturally, to create the highest risk portfolio the stock with the combination of sufficiently high risk and correlation values will receive the largest investment share as this combination will contribute the majority risk to the portfolio (which needs to be as large as possible). An investment weight of this magnitude in any other of the stock would contribute a smaller level of risk to the overall portfolio risk.
Figure 5
Losing Money
How much money will it lose over 100 days? The portfolio is expected to lose 0.00469 of its value daily, although the high-risk nature of the portfolio may cause this to change significantly. The stock markets trade for approximately 68 days out of the 100 day period between 1 December and 10 March (Business Days, 2009).
The portfolio is expected to lose approximately $27,380 of the initial $100,000 investment after 100 days, with the expected value of the portfolio being approximately $72,620 by the end of trading on 10 March. Again this value is only an estimate because the a higher-risk portfolio has been constructed and may vary significantly due to this and other factors such as market risk.
*$1 is assumed to equal £1 for the analysis
Appendix
A: Initial list of stocks considered from research
AAPL, AMD, JCI, TM, GM, F, DOW, WOW.F, JCP, LAN.L, DSGI.L, BRBY.L, DEB.L, HOME.L, CPR.L, ALY.L, JJB.L, RMV.L, BWY.L, BDEV.L, BVS.L, RDW.L, LII.L, JMAT.L, PHRX.L
B:The Portfolio
The image above is a screenshot of the portfolio in Excel. A list of possible portfolios made up different weightings is listed at the top. Each portfolio row has its associated daily return, variance and standard deviation listed, with the standard deviation calculated by expanding the portfolio risk equation for five stocks. The selected portfolio is highlighted in yellow.
The expected value is the sum of the weighted average values in the portfolio, with individual averages as well as standard deviations being determined using the AVERAGE and STDEV functions in excel on historical return data calculated from daily pricing data for the year up to 1 December 2008. These were downloaded from Yahoo Finance.
The expected return over the 100 day period is calculated using the parametric method equation using the daily expected return (-0.47%) and the number of trading days (68).
The formula “=POWER(1+C152,68)-1” is entered into the 68 Days Exp.Return cell, and is the 1 + the daily return to the power of the number of total trading days, taking away 1 at the end, resulting in the expected return over this period being approximately -27.35%.
By the end of 10 March 2009 the portfolio is estimated to have lost 27.53% of the initial $100,000, with the monetary value of this found by multiplying the investment by the return resulting in a $27,353 loss. Therefore the portfolio is estimated to be worth $72,646 approximately at the end of 10 March.
Using the percentage weightings and stock prices on 1 December 2008 the number of stocks to purchase in each company can be found and these can also be seen in the screenshot.
References
Britain's sinking economy. (2008, July 3). Retrieved December 12, 2008, from economist.com:
http://www.economist.com/opinion/displaystory.cfm?story_id=11670314
Business Days. (2009). Retrieved 27 January, 2009, from London Stock Exchange:
http://www.londonstockexchange.com/en-gb/about/cooverview/businessdays/
Different Types of Risk. (2008). Retrieved December 12, 2008, from Investopedia:
http://www.investopedia.com/university/risk/risk2.asp
Efficient Frontier. (2009). Retrieved January 27, 2009, from Investopedia:
http://www.investopedia.com/terms/e/efficientfrontier.asp
Fears over advert system privacy. (2008, April 15). Retrieved December 28, 2008, from BBC News:
http://news.bbc.co.uk/1/hi/technology/7349715.stm
Hard sell, hard times. (2008, December 11). Retrieved December 28, 2008, from economist.com:
http://www.economist.com/world/britain/displaystory.cfm?story_id=12781173
Hedge funds make £18bn loss on VW. (2008, October 29). Retrieved December 12, 2008, from BBC News:
http://news.bbc.co.uk/1/hi/business/7697082.stm
Pimlott, D. (2008, December 18). Retail sales growth at three-year low. Retrieved December 28, 2008, from FT.com:
http://www.ft.com/cms/s/0/ffa7266c-ccec-11dd-9905-000077b07658.html
UK in recession as economy slides. (2009, January 29). Retrieved January 29, 2009, from BBC News:
http://news.bbc.co.uk/1/hi/business/7846266.stm
US car giants report large losses . (2008, November 17). Retrieved December 28, 2008, from BBC News:
http://news.bbc.co.uk/1/hi/business/7715896.stm
What does risk mean? (2009). Retrieved January 30, 2009, from Investopedia:
http://www.investopedia.com/terms/r/risk.asp
