# Glossary

### Statistical Measures

Variance

Variance is a measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean and is always non-negative.

Mathematically the Variance is calculated as the average squared difference of each number from the mean.

Correlation

Correlation expresses the mutual relation of two or more things. In statistics, it is a single number, assuming values between +1 and -1, which measures the degree of a linear relationship between two random variables or two sets of data.

The correlation is +1 if two variables always move proportionally to one another in the same direction. This is called perfect positive correlation.

The correlation is -1 if two variables always move proportionally to one another in opposite directions. This is called perfect negative correlation.

If the variables have no apparent relationship then the correlation is said to be 0.

Volatility

Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can be measured by using the standard deviation between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security as the more broad the distribution of returns.

Standard Deviation

Standard Deviation is a measure to quantify the amount of variation or dispersion in a set of data values. Its symbol is the greek letter sigma (σ) and can be calculated by finding the square root of the Variance.

When the values are tightly bunched together, then the bell-shaped curve is steep and the standard deviation is small. When the values are spread apart, the bell curve is relatively broad which means you have a relatively large standard deviation.

Liquidity

Liquidity within financial markets refers to the number and size of buyers and sellers within the marketplace. The more liquid a security is, the easier it is to buy or sell without significant price impact. This is important becasue if a security is illiquid, when trading a large amount the price may move significantly during the execution of the order.

For example – A large ETF such as the Vanguard S&P500 ETF is much more liquid than an individual stock or share.

At Scalable Capital we invest only into highly liquid ETFs which track broad indices.

Simple Return vs Time-Weighted Return

Simple Return is calculated by taking the absolute return over a period and dividing by the amount invested.

E.g. if a portfolio has £15,000 in it and makes an absolute return of £2,000 over a 1 year period then the Simple Return = £2,000 / £15 ,000 = 13.33%

Simple return does not account for when additional payments or withdrawals are made.

E.g. if in the example above an additional deposit of £40,000 was made half way through the year and the second half of the year returned £5,000, then the Simple Return = (£2,000 + £5,000) / (£15,000 + £40,000) = 12.72%

Here the return seems artificially low because the simple return assumes the additional deposit was part of the initial investment.

Time-Weighted Return separates returns into different sub periods to take away the effect of deposits and withdrawals at different times. Hence the name “time-weighted”.

E.g. using the example above the two periods would be broken down to £15,000 returning £2,000 and the £57,000 returning £5,000.

Time Weighted Return = ( (£2,000 / £15,000) +1 )* ( (£62,000-57,000 / £57,000) +1) – 1 = 23.27%

The Time-Weighted Return is a more accurate reflection of the overall performance of an investment portfolio because it is not distorted by the impact of payments and withdrawals. this make it much more useful for comparing the performance of different portfolios.

Formulas:

Simple Return = (V1 – V0) / V0 = (Value at End – Value at Start) / Value at Start

Time Weighted Return is as follows:

Formula for each Sub-Period (SP1) = (V1 – V0 – D + W) / V0 = (Value at end – Value at start – Deposits + Withdrawals) / Value at start

Formula for whole period = [(SP1 + 1) (SP2 + 1) ….. (SPN +1)] -1