In our first articles we analyzed 10 companies from Technology Industry. These companies are: Yahoo, Twitter, LinkedIn, IBM, AT&T, Priceline, MTS, NTT, Activision Blizzard and ePlus. Now we need to analyze our portfolio. In the process of creation of this portfolio, we mostly based our analysis on business factors. We used fundamental indicators to either short sell or buy the company. Because of this approach, we mostly ignored or gave little value to the past price movements of the shares. That’s why the results of quantitative analysis will differ from those of fundamental. Therefore, we divided our portfolio analysis on two parts: 1) fundamental and 2) quantitative. Let's start from the fundamental analysis: 1. Portfolio analysis: Fundamental way As we know, core business of the companies from our portfolio, we should make some boundaries. In the case if the company goes beyond established boundaries, investor should close this position. So, we need to make these boundaries, which will differ from company to company. Mostly these boundaries are based on intrinsic value of the company. While analyzing these 10 shares, we have already calculated intrinsic values of companies. 1) Yahoo! Intrinsic Value - between $40 and $52 per share This investment, we consider as speculative, because we want to make sure profit on this position, as market undervalues Yahoo! shares before spin-off. Nature of this position suggests that investment should be medium-term.Recent news made us more optimistic on this position, as activist investor try to extract one of the companies in order to show intrinsic value of the company. Therefore boundaries for this investment: 1. Price of share is above range of $40-45. 2. Company will not extract its business within next 6 months. 2) Twitter Intrinsic Value - between $2 and $5 per share We go short for Twitter. Such investment always has greater risks, as they can made infinite losses. We recommend to buy American put-options on the prices between 10-15$ for the next two years. Such investment can make losses in the short-term, as market can be irrational very long. We think that investor can just run out of money, while waiting adjustment of market value. Therefore, investor should have first signs of future downfall within the year. Also, we will close our positions in the higher bounds, because we intend to close it, as fast as we can. By this strategy, we decrease our risks. So boundary is: 1. Price of share will not fell below $20 after 1 year 2. Company suddenly starts to make money (P/E will be lower than 20) 3)Priceline Intrinsic Value - $700 and $840 per share We recommend to short sell Priceline company. In this case we use same put-option strategy with same suggestions. Also, high prices of shares make this investment uncomfortable for small investors and make shares potentially more volatile. Company can solve this problem with dilution of shares, which will be considered as good sign. 1.Price of share will not fell below $1000 after 1 year 2. Company will announce dilution 4) MTS Intrinsic Value - between $10,5 and 23 per share We go long for this company as think that investors now are too bearish on it. This type of investment is called "contrarian" and based on strategy of famous David Dreman. Criteria of such companies, made our boundaries, which are: 1. The P/E of a company should be in the bottom 20% of the overall market. 2. The P/CF of a company should be in the bottom 20% of the overall market. 3. The company should have a high ROE, as this helps to ensure that there are no structural flaws in the company. ROE should be greater than the top one third of ROE from among the top 1500 large cap stocks. 5) IBM Intrinsic Value - between $225 and $290 per share Prices of company are in the decline for the past year and reached $139 per share. We think that this is Peter Lynch case, when strong company is undervalued by investors. In this case they are too strongly reflected on the decreasing sales. This also creates some limits, after which, investor should sell stocks: 1. When inventories increase faster than sales, this is a red flag. However, an increase of up to 5% is considered bearable if all other ratios appear attractive. 2. The Yield of IBM should be high, which includes being higher than the S&P average. 3. PEG is lower than 1. PEG can be based on the average of the 3, 4 and 5 year historical EPS growth rates. 6) ePlus Intrinsic Value - between $120 and $140 per share In the case of ePlus, we think that investor underestimates growth of the company. This fact also means that it is Peter Lynch case. This fact also means that company will have similar to IBM boundaries: 1. When inventories increase faster than sales, it is a red flag. However an increase of up to 5% is considered bearable if all other ratios appear attractive. 2. Average earnings growth for the last 3 years is in the range of 20% to 50. 3. PEG is lower than 1. PEG can be based on the average of the 3, 4 and 5 year historical EPS growth rates. 7) AT&T Intrinsic Value -between $38 and $41 per share In the case of AT&T, intrinsic value will not play huge role. Because of the fact that we intend to earn money on the dividends received, rather on the capital gain. So, in this case, we will have limits connected with capability of company to pay dividends: 1. Payout Ratio will go below 70% 2.AT&T will not be included in the top 50 market leaders that have highest dividend yield. 8) Activision Blizzard Intrinsic Value -between $45 and $60 per share Case of Activision Blizzard is close to the ePlus case, as it is undervalued growth stock. So, this is Peter Lynch case. But in this case as company does not depend on inventory so much, criteria change and will reflect possible overvaluation, which often goes with growth of companies. Limits for this company are: 1. P/E remains below 40. 2. PEG is lower than 1. PEG can be based on the average of the 3, 4 and 5 year historical EPS growth rates. 3. Average earnings growth for the last 3 years is in the range of 20% to 50% 9) LinkedIn Intrinsic Value -between $22 and $104 per share We think that LinkedIn is overpriced. Therefore, we go short sell on it. In this case we use same put-option strategy as we used in the Priceline and Twitter cases with same suggestions. The problem is that price of LinkedIn is likely to increase in the nearest future. Therefore, some corrections on boundaries should be made: 1. Price of share will not fall below $220 after 1,5 year 2. Company suddenly starts to make money (P/E will be lower than 20) 10) NTT Intrinsic Value -between $42 and $65 per share As in the case of AT&T, NTT's intrinsic value will not play huge role. Therefore, limits of the company are similar to the limits of AT&T: 1. The company's cash flow per share must be greater than the mean of the market cash flow per share. 2. A company's trailing 12 month sales are required to be 1.5 times greater than the mean of the market's trailing 12 month sales. 3.AT&T will not be included in the top 50 market leaders that have highest dividend yield. Return You should notice that we gave ranges of the intrinsic value. We made this for purpose. Firstly, no one knows TRUE EXACT intrinsic value of the share, so the range of intrinsic values makes better picture than one exact number.Secondly, by giving ranges, we for ourselves make ranges after which we decide to close position. For example, if IBM stock will go over 290$, it is very likely that we will sell it. Now, we take in the consideration dividends of the shares. We made predicted dividend gain for the next 5 years: Calculations suggest that you will fully return your money only on dividends almost in 5 years. We think that such forecast is quite optimistic. However, we think that our strategy of choosing companies with solid dividend payments works goodly. It can be more appreciable, as we think that in future years, there is high probability of next crisis on the market or, at least, correction. Next we calculate capital gain based on calculated intrinsic value of stocks. Initially, we calculated lower intrinsic values case: Then we did it again for higher values: You can see that short positions on Twitter, Priceline and LinkedIn can make very attractive returns within 2 years.We think that this high returns compensate riskiness of these positions. Also, return on MTS(MBT) was one of the highest in the both cases. But this investment has currency risk, as MTS works in the rubble. However, we think, even in the case of currency depreciation, net income of MTS will be adjusted in the long run. Overall, our portfolio can be divided on three parts: 1) High-growth undervalued tech companies. 2) Dividend stocks with opportunity to future growth. 3) Overvalued internet companies. From the fundamental point of view, we think that these position have low risks and can gain high returns, as we made solid analysis on these 10 companies. Warren Buffet tells that investment will have low risk and high return, if investor made a deep analysis of company. We agree with him. All our fundamental analysis was based on the basic math, which can be made by student of 8th grade. Now we go to the advancedmath analysis, linear algebra andprogramming. All theses stuff will be needed for the second way of analyzing our portfolio. 2) Portfolio Analysis: Quantitative way Financial markets are complex adaptive systems which are almost always indistinguishable from random processes. That said markets do exhibit quantifiable factors such as the value, mean-reversion, firm-size, and momentum factors, which are believed to drive the returns in the market. Fundamentally this is because they drive supply and demand for securities. Quantitative analysis is about building computational models which can be used to predict, with some error margin, what the markets are likely to do given a number of inputs. Most machine learning models are optimization models. A simple optimization problem will consist of input variables (model parameters), and output quantities, and constraints on either the inputs, outputs, or both. Essentially the problem becomes, how can we adjust the model parameters in such a way that the output quantity is optimized. For most financial models the quantity being optimized is a measure of risk-adjusted return. Risk-adjusted returns measure how many units of excess return are expected to be generated from however many units of risk. Excess return is the return of the investment above either a benchmark, risk-free rate of return, or some minimum required rate of return. Risk has many faces and most measures of risk-adjusted return will differ only in their definition and treatment of risk popular measures include beta, volatility, shortfall risk, draw-down risk, and lower partial moments. That said, generally speaking risk in any investment is the probability of loss. We will use several ratios to show performance of out models. Volatility is for a given period of time standard deviation, sigma, measures the historical variance (average of the squared deviations) of the returns from the mean return, Ој, over that period of time. The formula for this is: Beta measures the relationship between the security returns, rS and the market, rM. High beta stocks are considered to be more risk whereas low beta stocks are considered to be less risky. The formula for this is: Drawdown is the maximum decrease in the value of the portfolio over a specific period of time. The Sharpe ratio, originally called the reward-to-variability ratio, was introduced in 1966 by William Sharpe as an extension of the Treynor ratio. The Sharpe ratio discounts the expected excess returns of a portfolio by the volatility of the returns. The information ratio is an extension of the Sharpe ratio which replaces the risk-free rate of return with the scalar expected return of a benchmark portfolio, E(rb). The Sortino ratio was proposed as a modification to the Sharpe ratio by Sortino and van der Meer in 1991. The Sortino ratio discounts the excess return of a portfolio above a target threshold by the volatility of downside returns, Оґ^2, instead of the volatility of all returns, Пѓ^2. The volatility of downside returns is equivalent to the square-root second-order lower partial moment of returns. You can find code for computing all ratios on ratios.py of our github. https://github.com/Yerzat/Crediton/blob/master/src/crediton/... There are a lot techniques for portfolio optimization. The most famous model is Modern Portfolio. MPT is widely used in practice in the financial industry and several of its creators won a Nobel memorial prize for the theory. But the weak side of the theory is that it is limited of use since it can only handle historical data. That's why mixed estimation models have appeared, which use both historical and subjective data as input, should in theory be a good fit for the systematic funds aiming for a dynamic and systematic way for how to allocate between their strategies, since these models base their allocations on historical data combined with subjective views about the future. The most famous is the Black Litterman model which was the first model to apply mixed estimations to financial data. Black Litterman model is a mathematical model for portfolio allocation developed in 1990 at Goldman Sachs by Fischer Black and Robert Litterman, and published in 1992. But both models have been widely challenged by fields such as behavioral economics. Both models assume that investors are rational and markets are efficient, that's why they define risk as the standard deviation of asset price fluctuation. One of the most underestimated feature of the financial asset distributions is their kurtosis. A rough approximation of the asset return distribution by the Normal distribution becomes often an evident exaggeration or misinterpretations of the facts. In next articles we will show how to use dynamic option hedging to reduce risks of fat tail distributions. Let's look at both approaches separately. 1) MPT MPT is a mathematical formulation of the concept of diversification in investing, with the aim of selecting a collection of investment assets that has lower overall risk than any other combination of assets with the same expected return. Creator of MPT, Harry Markowitz proposed mean-variance optimization as the solution to the optimization problem. Mean-variance optimization seeks to maximize the expected return for any given level of risk (risk tolerance) or minimize the risk for any given level of expected return. The algorithm constructs an efficient frontier of allocations and allows us to choose an allocation based on risk preference. You can see python code mtp.py on our github. https://github.com/Yerzat/Crediton/blob/master/src/crediton/... Let's do backtesting on real market data. We are using quantopian platform which is used by python developers to create algo-trading strategies and real time robots. Quantopian provides minute-granularity historical data on the stock prices from 01/03/2002 until today. MPT with risk tolerance equals to 10% from 01/03/2002 to 02/12/2015 MTP with risk tolerance equals to 20% from 01/03/2002 to 02/12/2015 In general, in both cases the MPT beat S&P. But Max Drawdown of even MPT model with 10% risk tolerance is quite big. Let's take a closer look at the cases of sharp decline. The first sharp decline was in late 2002 and early 2003. The second was in the first half of 2009. The drawdowns were big since MPT is based on a normal distribution. But the latest study researches show that the markets are sometimes described by fat tail distributions. Nassem Taleb in his book "Silent Risk" shows how to use dynamic option hedging for fat tail distributions. We are going to use his technique in next articles. 2) Black Litterman model Black Litterman starts with the equilibrium assumption that the asset allocation of a representative agent should be proportional to the market values of the available assets, and then modifies that to take into account the 'views' (i.e., the specific opinions about asset returns) of the investor in question to arrive at a bespoke asset allocation. It overcame this problem by not requiring the user to input estimates of expected return; instead it assumes that the initial expected returns are whatever is required so that the equilibrium asset allocation is equal to what we observe in the markets. The user is only required to state how his assumptions about expected returns differ from the market's and to state his degree of confidence in the alternative assumptions. From this, the Black Litterman method computes the desired (mean-variance efficient) asset allocation. Since IPO of LinkedIn was in 2012 and the IPO of Twitter in 2013 and we have done fundamental analysis of our portfolio for the past 5 years, we will do backtesting from 2010/01/01 to 2015/12/02. The code of Black Litterman model BLM.py -> https://github.com/Yerzat/Crediton/blob/master/src/crediton/... As you can see volatility is just 0.16 and max drawdown is 14.9%. Comparing performance of Black Litterman with MTP for the same period we can sum up: Conclusion. Portfolio strategies will depend on the type of investor. More aggressive investor can make higher return with higher risks. When risk-averse investors can take low-volatile low return strategy. We showed that each type of investor can create portfolio from given 10 assets. If Investor want to be sure in the return with exact risk of the portfolio, he can use one of the strategies from quantitative analyze. When in the case of fundamental investor, he can use suggestions from the first part of portfolio analysis.