Risk & Return Table

Return and Risk: While analyzing past performances of stocks, it can not be expected that they will keep this performance in future. But it can be a good baseline if the analyze is made on a long term for creating an ideal opinion about their future performances. Similarly, standard deviaton of past data can give an idea about risks of various investments. A preference which is between return and risk must be made during investment preference. Choosing stocks which have high return and low risk can contribute to accuracy of investment. Besides, not chosing stocks which have high risk and low return can be more available. Generally, stocks which have high return also have high risk.

Expected Return: Gives the geometrical average of stocks’ daily returns. Geometrical average is calculated by multiplying n times return and taking the n degree root of it:

Square Root [(100+100)*(100-50)] - 100 = %0.

Geometrical Average = ( (1+x1)*(1+x2)*(1+x3)*...*(1+xn) )(1/n) -1

Average Return: : Gives the arithmetical average of stocks’ daily returns. Two different methods can be used for calculation of return. These are arithmetical and geometrical averages. For example, let the returns of a financial instrument be in the board below:

Year	Price	Annual Return (%)
1	100	-
2	200	100
3	100	-50

If the return is calculated with arithmetical average :

[100 + (-50)] / 2 = %25 is the return.

If the returns are x1,x2,x3,...,xn

Arithmetical Average=(x1+x2+x3+...+xn)/n

But the point that have to be cared is; the price on 3th year is equal to the price on 1st year. Despite calculated return is %25, accrued return is %0.

Because this problem of arithmetic average, geometric average is used as second way.

Gives the daily geometrical average of stocks. Geometrical average is calculated by taking square root of multiplying of n times return :

Square Root[(100+100)*(100-50)] - 100 = %0

Geometrical Average = ( (1+x1)*(1+x2)*(1+x3)*...*(1+xn) )(1/n) -1

Risk (Standard Deviation): Gives the standard deviation of returns. Risk is determined as uncertainy in case of accrual of a financial asset’s return.

Investors take risk only in case of an extra return. For example, an investor earns 10.000 $ for 50.000 $ that he/she invested on %50 possibility, also losing 10.000 $ on %50 possibility for the same money. Because of the decreasing marginal benefit of investment, satisfaction of the investment’s increase to 60.000 $ will be more than investment’s decrease to 40.000 $. Decreasing marginal benefit denotes that investors are avoiding from risk. Generally investors take risk, but only for more return. In case of variability is accepted as a measurement for risk, it is possible to calculate risk with statistical methods. The method which is used in calculation of risk is standard deviation of expected return or variance of it. It can be easily stated that because of standard deviation is the square root of variance, both methods are saying the same thing.

Risk = Square Root (£(xi-Getiri)2/(n-1))

Expected Return / Risk: It simplifies that understanding the relationship between stock returns and risk. It can be available that not preferring the stocks which have low Expected Return / Risk ratio. It will be seen that risk increases when the wanted return increased during making a selection among the stocks which have high Return / Risk ratio. Thereby, it will be seen that when the expected benefit increases, taken risk will be increased.

Beta Coefficient: Beta coefficient of a stock is a measurement about it’s market risk. Beta coefficient of stock shows that sensitivity of it compared to index.

Beta Katsayısı: ß

if ß=1 stock’s movement is same with index. (Average Risk)

if ß<1 stock’s movement is slower than index. (Low risk, Low volatility)

if ß>1 stock’s movement is faster than index. (More risked, high volatility)

If the beta coefficient of stock is 1, it is expected that when index increased %10, stock will increase %10 and when index is decreased %10, stock will decrease %10. If the beta coefficient of a stock is 0.5, it is expected that when index increased %10, stock will increase %5 and when index is decreased %10, stock will decrease %5. Also if the beta coefficient of a stock is 1.5, it is expected that when index is increased %10, stock will increase %15 and when index is decreased %10, stock will decrease %15.

Risk-Beta-Return Maps

Risk-Return and Beta-Return Maps

On Vertical axis, percentage returns of stocks will take place and in horizontal axis, risk or beta coefficients of stocks will take place. Board is divided to four parts because of there will be a complexity if so many stocks are selected. You can analyze it detailed by selecting any part. Numbers are given to stocks on maps. You can see the BIST codes of stocks which are being represented by these numbers.

Stocks which have positive expected returns are showed with green boxes and stocks which have negative expected retuns are showed with red boxes. Selected index is also showed with blue box. Horizontal discontinuous red line on map is 0 return bound. Also blue discontinuous lines are showing the market risk (selected index) and return.

Interpretation of Maps

• Risk-Return Map: Seeing stock returns and risks as graphics simplifies that comparing risks and returns. Areas that stock risk and returns are came together can be seen. Thereby, it can be easily seen that more or less risked stocks according to other stocks and stocks which have more or less return according to the others.

• Beta-Return Map: Beta coefficient of stocks are the indicators of theirs market risks. The more beta coefficient of stocks is bigger, the more market risk will be bigger.

Reporting Options Usage

Reporting screens are designed for getting attractive stocks of the day fastly to the screen according the various criterions without the difficulty of returning menu again or going to another page.

• Market Index: Beta coefficient and alpha statistics of stocks are calculated by using the selected index.

• Stocks which will be involved to calculation:You can select all stocks if you think market index is showing enough the status on market. Otherwise, select the stocks which involved to index.

• Day: Number of closings which will be used for calculation of statistics.

• Map Type: Select which you want to see between Risk-Return or Beta-Return maps.

• Board:: Click to see the statistics on board

• Map: Click to see the graphics of Risk-Return or Beta-Return maps.