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Literature Review On The Choice Of Stocks


This report summarises our investment approaches to form a fund in the simulated market. Data were timely and freely available for research. Also, insider trading was impossible to happen. By not allowing investments of more than 10% of a fund’s total money market movements cannot be resulted due to major investments in specific stocks. All he above secured the market efficiency (Elton et al, 2011).

In the first part all theoretical approaches are synthesized in order the reader to have a more holistic point of view in respects to the background used to so investments to take place. Next the theories explained on the literature review part are applied and several portfolios were formed and managed. Lastly, the conclusion part includes an overall evaluation of the fund relative to the average of all funds. Also negative aspects of the strategy formation and the market structure are analysed

Literature Review-Choice of Stocks

Fund allocated to outperform the Global Index as includes all the assets of the market, is the most diversified and has the largest capitalisation in Market-Class. We chose assets based on the business cycle theory, diversification theory and based on their beta coefficient.

The business cycle influences security prices and deals with the variation of economic activity over time. Business cycle has two stages, economic expansion and contraction. Cycles depend on both cyclical and structural changes and deviate a lot (Reilly & Brown, 2006). Investors attempt to locate the sector which will grow in the next cycle phase.

Different business sectors perform differently along business cycles (Reilly & Brown, 2006). Towards the end of a recession, investments on financial assets are booming because the earnings are expected to rise due to the rising demand for loans. When the economy starts recovering, investments in consumer durable goods like automobiles are appealing. Consumers are more optimistic about their income and willing to spend. This recovery tempts companies, like semiconductors and food companies to invest to satisfy rising demand. At the boom period, increases in aggregate demand will cause inflation rises. At this stage, investors prefer basic materials stocks, like oil and utility. When the economic activity declines industries, like pharmaceuticals, that their demand is unaffected are preferred.

By investing in all sectors of Market-Class, not only we hedged against changes of taste according to business cycles but also we diversified our portfolio across industries and countries. Adding more assets can eliminate most of risk but after a point it is ineffectively because the following equation [1] for the portfolio variance applies:

As the N goes to infinity the first part becomes zero but the second regresses to the average of covariance. Consequently, we invested in 10 stocks, 2 in every sector, according to their beta.

According to Elton et al (2011) investors must compensated only for the systemic risk of a security, not its diversifiable non-systemic risk. The ‘beta’ indicates the non-diversifiable risk of a stock and measures the sensitivity of its return in respects to the market portfolio return, in that case the Global Index (Elton et al, 2011). The equation [2] to find betas is:

The slope between the returns of a stock and the returns of the market in the same period can be used to find beta. Firstly we have to find the simple returns as the latest are easier to compute and are realistic with old data (ten years annual data in that case), something that applies for average returns and variances (Reilly & & Brown, 2006). The equation [3] for simple returns is:

The “slope” function computes beta. We risked and invested in the stocks with the highest beta because we have diversified across industries and countries. Figure 1 illustrates the 10 chosen stocks with the highest beta.

Variance-Covariance Matrix

The portfolio inputs were the adjusted close prices for every stock and index in annual intervals for ten years. As risk-free rate we used the yield to maturity on the 1-year bond because our investment horizon was one year. Then, we calculated the simple returns using the formula 1.2, the average returns using the ‘=Average’ function in excel and the variance using the ‘=VAR’ function. With the average returns we can construct the Variance-Covariance (VCV) matrix, which sums the risk of all the assets of the portfolio taken into account the covariances among them. Its diagonal elements consist of the variances of stocks and the off-diagonal elements consist of the covariance between pairs of assets (Shen J., 2010). The ‘=mmult’ and ‘=transpose’ functions in excel where used to calculate the VCV matrix. With the incorporation of excel to calculate the VCV matrix find how stocks are combined and correlate in a portfolio (Benninga S., 2008).

However, using historical data to calculate returns and standard deviations can produce very noisy estimates of their actual values. This is because data may not be relevant today and secondly, they overestimate covariance between two assets. Also, there is difficultly in predicting the Global Minimum Variance Frontier from the VCV matrix (Benninga S., 2008). The previous mentioned drawbacks lead to implausible portfolio asset weights. The following section analysis the most popular technique to reduce the estimation error.

The Shrinkage Method

This technique is mainly used to ‘shrink’ the estimation error and its implementation is straightforward. It assumes that “the shrinkage VCV matrix is a convex combination of the sample VCV matrix and some other VCV matrix” (Benninga S., 2008, (P.308)). The other VCV matrix is the inverse of the sample VCV matrix containing only variances and the covariances are equal to zero. The shrinkage VCV matrix is the weighted average between the VCV matrices of the sample and its inverse. A shrinkage estimator (λ) is required; to compute the new shrinkage matrix. This factor is the weight given to the sample VCV. The following equation [4] illustrates how the shrinkage VCV is computed:

Benninga S. (2008) argues that the shrinkage estimator lies between 0 and 1, and that any changes in λ make the GMVP to change and moves the efficient frontier to the right, hence make it less risky. When λ is set equal to one the GMVP obtained should be the same as the GMVP obtained by the initial VCV matrix. Furthermore, he suggests that the value of λ should be such so that the weights of the stocks constituting the GMVP are all positive. Using the ‘data table’ function, we found, the suitable shrinkage factors for every round of the game. Finally we compute the Shrinkage VCV matrix using the shrinkage estimator.

The major drawback of the Shrinkage method is the difficultly in determining the proper shrinkage estimator. Moreover, the assumption that the covariances of the ‘other’ VCV matrix are equal to zero is not well supported.


This method is a quantitative approach minimizing the estimation error occurring due to unintuitive weights on portfolio (Maginn et al, 2007). It results in more well diversified portfolio across selected stocks and epitomises the active portfolio management because it allows to investors to derive optimal weights by incorporating their opinions-information. There are two parts, the first deals with what the market things and the second adjust the findings for the investors’ opinions (Benninga, 2008).

Black-Litterman model assumes markets are efficient and consequently, close to reality. To calculate the expected returns implied by the Black-Litterman model, we use the following formulae [5] :

Lambda can be calculated by the equation [6] :

Portfolio weights given from the formula [7] :

To calculate the expected returns implied by the market we must identify the capitalisation of the stocks and divide each capitalisation with the sum of all capitalisations, thus find the market weights (Benninga, 2008). We did this by multiplying the shares outstanding with the stock price, at the specific day (Reilly & Brown, 2006). Also, we assumed that the anticipated benchmark return is annually 12%. The expected return of the benchmark portfolio is calculated using the formula 1.3. We make this assumption because the formula 1.3 can only be used when the expected return is bigger than the risk-free rate (Benninga, 2008). Otherwise the equation is negative and has no meaning. Finally, we computed the benchmark portfolio returns with the formula [8] :

To make this fund actively managed we must derive the expected returns of one or more stocks by adding our opinions. However, having a different opinion for expected returns in one or more stocks, leads to a different portfolio weight allocation because stocks are correlated. To adjust the expected returns we found by using equation 1.6, we must add to them our opinion named delta. To form these opinions we found the required return k of each stock based on the dividend discount model. The equation [9] is:

Growth rate formula [10] :

ROE can be found [11] :

Payout ratio [12] can be found by:

We applied the formulas 1.9 and 1.10 for all of the last ten years and then summarised the results for that period. These averages are used to compute the growth rate based on the last ten years, as mentioned before. Finally we found the required return for each stock in each round [13] . If the required return was higher than the expected return found by the first step, this was our opinion-delta.

According to Benninga (2008) to compute the expected return we must take also into account that all stocks are correlated among them. The result of the optimal weights and expected returns must adjust. Τhe following formula [14] was used to calculate the adjusted expected returns:

For the equation 1.11 we formed a 10x10 matrix by calculating the covariance (ri,rj)/ variance(rj) for each pair of stocks. At the last part we used the ‘solver’ function to find the optimal weights with our opinions and accounting for the correlation among stocks, by minimising the sum of squared opinions-deltas (Benninga, 2008). We did this procedure in every round by changing the data and using only the last ten year to be more relevant. It must be mentioned that throughout the rounds we used constraints to the “solver” according to good or bad news for our stocks in order to take advantage of them and put more or less weight.

Relative Valuation Techniques

The relative valuation techniques determine the value of non-fixed income assets by direct comparison with assets on the base that there are certain variables influencing the movement of prices (Reilly & & Brown, 2006). These variables include earnings, cash flows, book values and sales. The ratios that are formed by incorporating the latest mentioned variables include the price to earnings, price to book value and price to sales. We used the first two as they are the most widely used (Reilly & & Brown, 2006).

The price to earnings ratio or earnings multiplier model is based on the concept that the value of any investment is the present value of future returns (Reilly & & Brown, 2006). It is the money an investor is willing to pay for every one pound of extra return he gets. The equation [15] that used is:

The price to book value is mainly used by banks as it shows the relation between the current price and the intrinsic value of the underlying asset (Reilly & & Brown, 2006). The equation [16] that computes this ratio is:

For both ratios the estimation of the earnings and book values is based on the growth rate of dividends. This is because the following equation [17] applies:

Although we computed the growth rate based on the financial statements when this rate used to compute the P/E and P/BV ratios produced slightly different results from the ones of the Market-Class. We assume that the latest are correct.

In order to do our analysis we divided P/E and P/BV of all stocks with the ratios of the respective industry as the financial and operation features must be more or less the same (Reilly & & Brown, 2006).

In respects to P/E evaluation, when the latest division produce a lower than one outcome then the specific stock is selling at discount and it is a good purchase (Reilly & & Brown, 2006). The opposite applies with a result higher than one. In respects to P/BV ratio when the division produces a higher than one outcome then the stock tends to have a good outcome in bad industry times (Elton et al, 2011).

Financial Analysis

In the last two rounds we also used financial analysis which included the research of the liquidity and the leverage of the firms the shares of which are sold in this simulated market. This analysis gives a useful insight on how the future of companies might be formed (Palepu et al, 2007).

We analysed the liquidity of the firms with the current ratio which illustrates the capability of the firm to repay its current obligations. The ratio is given by the following equation [18] :

A ratio above one advocates the well being of a firm.

Finally we checked the leverage of firms by calculating the debt to equity ratio. It must be highlighted that the debt must not consider totally bad aspect. This is because debt is tax deductable for firms and also the indentures, the contracts, signed between the company and its lenders impose control making them less risk-tolerant (Palepu et al, 2007). The equation [19] used to find this ratio is:

For the above mentioned reasons we preferred companies that have a proportion of debt as the latest might have a more riskless future.

At this section we provided the theoretical background we use in order to make our investment decision. The next part summarises the outcomes of the previous mentioned procedures.

Rounds Summary

Round 1

As the main goal of the fund is to beat the benchmark the initial step which was taken at this point was selling the MC Global Index (MCGI) in amount of ($34,388,998.09) and the proceeds were used to invest in selected stocks obtained by beta estimation analysis. Onwards taking into consideration Black-Litterman results and using Excel solver the weights and amount of money invested were found. For calculating the average and variance for each stock by using the relative functions of excel. The combined findings were used for the variance-covariance matrix and we applied shrinkage variable to reduce estimation error. As it was explained previously, Shrinkage VCV matrix formula was used and the best lambda according to the data we had calculated as 0.1 for this round. The expected returns of the market from Figure 1-1 were calculated using the formula 1.3, the Risk free rate was the yield to maturity of the 1 year T-Bond.

Figure 1-1

To form the opinions and create an active fund the required returns were found according to financial statements for the last ten years. To find the inputs of formula 1.7 we had to find the growth, ROE and payout ratios by incorporating formulas 1.8, 1.9 and 1.10 respectively. The next step was to form our opinions by subtracting results obtained by using formula 1.7 from the results found from the formula 1.3 which are shown below in figure 1-2.

Figure 1-2

Solver function found the optimized portfolio opinions. Taking into consideration the correlation of each stock with the other stocks of the portfolio we put into solver the matrix which was constructed by using the formula 1.11. We put some constraints in “solver” according to news. For the stocks ICOU and SOJU the weights optimization was driven by the news given for this year by Market-class. The Soda Johnson (SOJU) was announced to have positive news about its new product line and as a result future growth prospect. On the other hand Icarus Oil (ICOU) reported a shut of one of its oil refinery which as a result might have negative impact on company’s income and the Alpha seekers fund respectively. To comply with the restriction of not investing more than 10% of the fund value and moreover the overall weight of the portfolio must be unity, we had to put two more constraints to Solver. Findings are illustrated in Figure 1-3.

Figure 1-3

According to the weights obtained it was found the money and the number of shares which needed to be invested in the round 1.

Figure 1-4

For better diversification and reducing the volatility of the portfolio it was decided to buy 1 year US T-bond (UST01A). The maturity of the bond was matched to the investment horizon of the fund. The remaining amount of funds available was held in cash in order to cover unexpected losses from current investment.

Investment in this round has shown weak results compared with all funds average total return, i.e -0.8% and -0.4% respectively. This can be explained by significant losses in market MC Global Index returns -4.4% as the fund contained 37% of the MCGI.

Round 2

Following the same strategy and analysis as it was used in the previous round the asset allocation for the year 2012 appeared to be in the following way:

Figure 2-1

Adding the data from the previous year to the model had changed some values in expected returns and other columns as well. The decision concerning how much money to invest was also adjusted to the previous round holdings and the number of shares and money invested were according to new weights obtained by Solver. The news for this period were given for Solaris Energy (SOLJ) and SodaJohnson (SOJU), both of them prognosticated positive expectations about stock price and return appreciation which was supposed to have a positive impact on fund returns. So the Solver constraints were put according to news for this round. For the year 2012 there was no investment in bonds because all the bonds were

The fund’s return for the year ended 2012 was 7.2% which is higher than the results from the year 2011. Furthermore fund has shown above average results in comparison with all funds average annual total return which is 6.38%. This can be explained by better portfolio rebalancing and diversification of the fund.

Round 3

For the following three weeks along with Black-Litterman method we included top down-approach to analyse the market from big picture all the way to individual stock and take advantage of mispriced stocks in accordance to their P/E ratio.

Decisions based on Black-Litterman approach were similarly made to that of previous weeks. For top down approach industry specific and market specific price-earning evaluations were made (figure 3-1). Accordingly we invested $6,000,000 in United States Index (USDI) as it was found undervalued

Figure 3-1

In Industry (figure 3-2) Evaluation Pharmaceuticals (PHRI) were found undervalued and $ 10,000,000 was invested in it.

Figure 3-2

In industry specific stock evaluation Janssen & Janssen (JNJU), NeoPharma SpA (NEOE) and Zenith PLC (ZENG) were found undervalued and $15,000,000 were invested in accordance to the weightage of their undervaluation (figure 3-3).

Figure 3-3

Round 4

Black-Litterman Approach and Top-Down Approach were followed similarly as in previous week. In this year again United States Index (USDI) was found undervalued. By looking at the price of last 5 years it was found to be very volatile and was decided to put a limit order at a rate of $43.00 per share for 35,000 shares as we already had 42903 shares of it from the previous year (figure 4-1).

Figure 4-1

In Industry evaluation we found Pharmaceuticals (PHRI) undervalued. Accordingly it was decided to invest that 30,000 more shares should be purchased as we already had 72,281 shares from the last year (figure 4-2).

Figure 4-2

In Industry specific stock evaluation of Pharmaceuticals Industry (PHRI), all of the five stocks of the industry were found undervalued. Accordingly we decided to invest in 5,125 shares of Janssen & Janssen (JNJU) as we already had 81,258 shares from last year, 46,610 shares in NeoPharma SpA (NEOE) and 111,515 shares in Zenith PLC (ZENG). We did not invested again in BIOU and BRUE again as they were already taken into consideration in Black-Litterman Approach (figure 4-3).

Figure 4-3

Round 5

Black-Litterman Approach and Top-Down Approach were followed as in previous weeks. In this year United States Index (USDI) and United Kingdom Index (GBPI) were found undervalued in accordance to Price Earning Evaluation. $13,000,000 was invested in both of the index according to the weight age of their undervaluation (figure 5-1).

Figure 5-1

In Industry Evaluation Oil & Gas (OILI) and Pharmaceuticals (PHRI) were found undervalued. Accordingly 5,135 shares of OILI were purchased and 33,900 shares were purchased of PHRI as we already had 112,560 from last year (figure 5-2).

Figure 5-2

In industry specific stock evaluation of Pharmaceuticals Industry (PHRI), Zenith PLC (ZENG) was found undervalued and 2,722 shares were purchased as we already had 35,520 shares from the previous year and in Oil & Gas Industry (OILI), Ixxon Inc (IXXU) and MAXI SA (MAXE) were found undervalued and accordingly $2,000,000 were invested in accordance to their weightage of undervaluation (figure 5-3, 5-4).

Figure 5-3

Figure 5-4

Round 6

To obtain the optimal portfolio by using Black-Litterman method, we need to found the Variance-covariance matrix first, and introducing shrinkage variable to reduce estimation error. The most important thing here is to calculate benchmark portfolio returns and their weights, with formula 1.5 and 1.6. Results are displayed:

We found the ‘delta’ by computing the differences between required return and Black-Litterman expected return, then set limitations based on news (good news on BIOU and COTU, bad news on AITE) and trading weights constraint. Using SOLVER, we get the final portfolio.

Figure 6-3

Figure 6-4

35,000,000 dollars were spending on those 10 stocks, another 35,000,000 dollars invested according to relative valuation method which is, mainly, earning multiplier. We recognize the P/E ratio of global index (MCGI) as 1, if regional or industry index to global index less than 1 means undervalued. We desire to benefit from the market recognize these kind of indices and adjust their price by holding them.

Figure 6-5

Figure 6-6

According to calculation, we invested in PHRI and also, we believe the stocks in within were undervalued. After the same procedure, two stocks fit our theory, however, BIOU already included in the 10 stocks, only ZENG should be purchased here, the result is showed following:

Figure 6-6

For the reason that bond yield exceed cash interest, we spend the rest $15,149,129.42 in UST30A. The annually coupon yield is 6%, which higher than interest rate, 4.31%, namely.

As a result, for this year, our portfolio return is 15.6%, while the MCGI’s return is 15.0%. We also beat the peers which reward 10.55% in average.

Round 7

In week 7 we form the opinion with the same methodology. After figured out delta, we take into account the impacts of news and believe the price of OAKG will benefit from the announcement that the cost of the company will reduced. The SOLVER gives the final weights of the optimized portfolio in figure 7-1.Thus we confirmed the investment order for this year in figure 7-2.

Figure 7-1

Figure 7-2

In this week, when calculating the P/E ratio, the results were negative. According to Reilly and Brown (2006) negative P/E ratio has no meaning in making investment decision, so we suspend relative valuation investment this week but spend on currency index due to the news that USD is weaken to JPY, EUR and GBP. So we sell all the USDI we already hold, which is $2,084,477.78, and buy EURI and JPYI for $5,085,505.75 and $5,056,191.05 respectively.

This year, we maintain the risk level and gain 4.9%, by contrast, the market return is 7.6% and all funds average return is 10.15%. However, our total asset is 143,170,162, still beyond average level, which is 136,462,422.

Round 8:

At this point we wanted to test the market with the relative valuation technique. We selected price-to-earnings ratio and price-to-book ratio as our selected benchmark. Furthermore, we considered current ratio and debt to equity ratio based upon financial analysis to have a better insight.

Market-Class provides the P/E and P/BV rations for every stock and industry. We divided companies’ P/E and P/BV ratios by those of industries’. Then accounted for ROE, liquidity, leverage and news. Finally, we made the buy-sell suggestion to our investment. The following five figures illustrate the analysis data for all five industries.

Figure 8-1

Figure 8-2

Figure 8-3

Figure 8-4

Figure 8-5

Besides investing the individual stock, we also considered the national index and industry index as well as the MC global index. We only looked at the P/E and P/BV ratios of these stocks. Figure 8-6 shows the decision result.

After knowing which stock to buy or sell then we should know how many shares of every stock we should buy or sell. First we get the market capitalization of the suggested stocks and times the total money of the market which is 100000000. Then we divided it by the stock price of that period to know exactly how much we should own. Finally, we compared it with data of 2017 year to get the difference to make the 2018 order which is shown as follows.

Figure 8-7

The following figure shows us the investment result for 2018 which is followed the title Year 2019.

Round 9:

This round is the last investment round of our task. The strategy for this round is similar with the previous round. As the situation changed then we changed the money we invested in the stocks. Furthermore, when deciding how much money to invest in each selected shares we used Excel “SOLVER” function to add some constrains to it. The following figures show what we did in our analysis.

Figure 9-1

Figure 9-2

Figure 9-3

Figure 9-4

Figure 9-5

Figure 9-6

The following figure is the outcome for the last investment round which is followed by the title Year 2020.

Broadly, we got similar good results but below average in the last rounds. The relative valuation technique proved to be good practice.


Generally Alpha Seekers fund generated positive returns, except round 2, peaking in the last round. Nonetheless, the fund return was below the average of all funds and especially in the last rounds was nowhere near the mean. A part of the fund created based on past data supported the argument that in an efficient market, abnormal return cannot be achieved by analysing past data.

Diversification has taken into consideration throughout the simulated rounds of the game. This explains why we tried to find optimal weights and weights that depicted the amount of undervaluation of a stock or an index so as to invest in many financial vehicles and reduce risk Results might advocate lost opportunities as other fund managers invested more heavily in few stocks and could not followed by the respective fund. In respects of lost opportunities, by incorporating many evaluation techniques, findings tend to cancel out each other. On one respect we gained a more holistic view of the non-fixed income assets and reduce risk, but on the other we did not take the risks and consequently the gains, as most funds did, to evaluate according to p/e ratio and news

Furthermore, our belief derived from the financial analysis for a crisis did not occur. Financial positions of many firms were weak but this was not an issue for the market and the price was ascending. An example was Henson-Kit Beverages which had a devastating current ratio but the stock price was rising.

Moreover, there were some behaviour finance mistakes. The major issue was the disposition effect that influenced our decisions and the related opportunity cost. We tended to “hold” losing stocks instead of selling them, realising a loss and invest the remaining money to recap (Elton et al, 2011).An example is the holding of Global Index after the wrong decision to sell it in the first round. The “locking” of the money in anticipation of a rise resulted on not making a better use of them and loss of momentum. This same applied for the pharmaceutical index in round 7.

The argument of Elton et al (2011) that there is no point of using an active strategy and trying to take opposite positions from the market was supported. Although, the theoretical background was solid, the rest of the market disagreed. Consequently, no shifts towards the funds interests occurred. When the fund invested a huge amount of money according to news outperformed the average but when it used the approaches discussed earlier did not aligned with the majority.

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