1. DATA TIME HORIZONS Read more
1.1 MONTHLY PRICE DATA
When monthly price data is used, we define the following time horizons:
1 month = last monthly quotation
6 months = last 6 monthly quotations
12 months = last 12 monthly quotations
Our calculations involve monthly averages as well as end of month prices. The table under section 2 shows which price is used for which raw material.
1.2 Daily price data
When daily price data is used, we define the following time horizons, considering the number of trading days in a certain period of time:
1 month = last 20 daily quotations
3 months = last 60 daily quotations
6 months = last 125 daily quotations
12 months = last 250 daily quotations
2. SPECIFIC RAW MATERIAL CONSIDERATIONS Read more
Raw material | Type of monthly price data | ||
Last day price | Month average price | ||
1 | Crude oil Brent | x | |
2 | Cruide oil WTI | x | |
3 | Natural gas EU (c.i.f.) | x | |
4 | Natural gas US (NYMEX) | x | |
5 | Cotton (A-Index) | x | |
6 | Cotton (ICE Futures U.S) | x | |
7 | Rice (5% Thailand) | x | |
8 | Rice (CBOT) | x | |
9 | Cattle (U.S. c.i.f.) | x | |
10 | Live Cattle (CME) | x | |
11 | Feeder Cattle (CME) | x | |
12 | Pork (CME) | x | |
13 | Chicken (US wholesale price) | x | |
14 | Wheat hrw (US f.o.b.) | x | |
15 | Wheat srw (US f.o.b.) | x | |
16 | Wheat (CBOT) | x | |
17 | Wheat (Euronext Paris) | x | |
18 | Corn (CBOT) | x | |
19 | Corn (US f.o.b.) | x | |
20 | Corn (Euronext Paris) | x | |
21 | Soybeans (CBOT) | x | |
22 | Soybeans (C.i.f. Rotterdam) | x | |
23 | Cocoa (ICCO) | x | |
24 | Cocoa (ICE Futures London) | x | |
25 | Sugar (NYBOT) | x | |
26 | Sugar (LIFFE) | x | |
27 | Sugar EU (c.i.f. Europe) | x | |
28 | Sugar US (c.i.f. US) | x | |
29 | Whole milk powder (f.o.b. Europe) | x | |
30 | Skimmed milk powder (f.o.b. Europe) | x | |
31 | Butter (f.o.b. Europe) | x | |
32 | Copper (LME) | x | |
33 | Aluminium (LME) | x | |
34 | Lead (LME) | x | |
35 | Zinc (LME) | x | |
36 | Nickel (LME) | x | |
37 | Gold (LBMA, pm) | x | |
38 | Silver (LBMA) | x |
3. RETURNS Read more
3.1 CALCULATION
In our calculations we use logarithmic returns (log returns).
For P1 = new price, P0 = old price, we calculate:
To show returns over the last 1, 3, 6 or 12 months, we add up the log returns for the respective period of time.
As compared to arithmetic returns, logarithmic returns have the advantage that the development can be approximated by the normal distribution. This also means that log returns are time additive:
This is important to several statistical methods and key figures like volatility.
3.2 ARITHMETIC RETURNS VS LOGARITHMIC RETURNS
The following simple example illustrates the problem with using arithmetic returns, as they are not time additive.
The price in period 0 = 1.
It rises by 15% (arithmetic return) and is 1.15 at the end of period 1.
Then the price drops again by 15% (arithmetic return) so it is 0.9775 at the end of period 2.
The overall change (arithmetic return) from period 0 to period 2 is -2.25%.
However the sum of the arithmetic returns is +15% -15% = 0.
Comparison to log returns:
The change from 1 to 1.15 equals a log return of +13.98% (ln(1.15/1)).
The change from 1.15 to 0.9775 equals a log return of -16.25% (ln(0.9775/1.15)).
The overall change (log return) from period 0 to period 2 is -2.28% (ln(0.9775/1)).
Finally the sum of log returns is also -2.28% (+13.98% – 16.25%).
4. VOLATILITY Read more
4.1 FUNDAMENTAL DEFINITION
Volatility is a measure for variation of price of a financial instrument over time. It is defined as the standard deviation of returns and serves as a risk measure. Commonly, the higher the volatility, the riskier the security. The symbol for volatility is σ (sigma), the same as for standard deviation.
The standard deviation (σ) of a data set is the square root of its variance (σ²). The variance is the average of the squared differences from the mean.
N = number of values; Xi = individual x values (x1, x2, etc.); μ = mean of all values
4.2 ANNUALIZED VOLATILITY
The annualized volatility σ is the standard deviation of the instrument’s yearly logarithmic returns.
The generalized volatility σT for time horizon T in years is expressed as:
Therefore, if the daily logarithmic returns of a stock have a standard deviation of σSD and the time period of returns is P, the annualized volatility is
We assume that P = 1/250 (there are 250 trading days in any given year). Then, if σSD = 0.01 the annualized volatility is:
4.3 OUR KEY FIGURES
Volatility (last 3 months) = the standard deviation of log returns of the last three months (daily price data), annualized by multiplication with √250.
Volatility (last 12 months) = the standard deviation of log returns of the last 12 months (monthly price data), annualized by multiplication with √12.
5. CORRELATIONS Read more
5.1 DEFINITION
The correlation describes to what extend two sets of data are linked to each other. When two sets of data have a high correlation they are strongly linked to each other.
Correlation can have a value between -1 and 1:
1: a perfect positive correlation; the values of two sets of data rise/fall together
-1: a perfect negative correlation; when one value decreases the other value increases
0: no correlation at all
5.2 CALCULATION
For our calculations we use the Pearson’s correlation coefficient:
Xi = individual x values (x1, x2, etc.); Yi = individual y values; Xm = mean of all x values; Ym = mean of all y values