# How different strategies have performed

Before you invest in anything it is prudent to first measure and analyse the expected risk against the potential reward of any given investment strategy. In this section we have done this work for you, and show all of the hypothetical back-tests of the guru strategies in an aggregated overview. Due to the fact that the analysed period includes two of the worst bear markets in recent history you will also get a sense of what the downside risk can be. Using five different professional methods for evaluating the data, we also explain in further detail what each method means and how to use it.

# Beta

Beta is a measure of the volatility or systematic risk of a portfolio in comparison to the market as a whole. Beta is calculated using a so-called statistical regression analysis. Think of beta as the tendency of a security's returns to respond to swings in the market. A beta of less than 1.0 means that the portfolio is expected being less volatile than the market. A beta of greater than 1.0 indicates that the portfolio is expected being more volatile than the market. For example, if a portfolio's beta is 1.2, it's theoretically 20% more volatile than the market. Many utility company (power, water etc.) stocks have a beta of less than 1, conversely, most high-tech stocks have a beta of greater than 1, offering the possibility of a higher rate of return, but also posing more risk. It is worth noting that a stock’s beta can also be negative, which means that the stock will move opposing to the market. If the market goes up, the stock will go down, and vice versa.
\beta = \frac{\text{cov}(R_a,R_b)}{\text{var}(R_b)}

R_a is the asset return, R_b is the return on a benchmark asset, \text{cov}(R_a,R_b) the covariance between the return of the portfolio and the return of the benchmark and var(R_b,) the variance of the benchmark.

# Calculations based on back-tested hypothetical performance since Jan 2000

Original formula

Original formula plus meetinvest positive price momentum rule

Data source: Bloomberg, Calculations: meetinvest

Disclaimer

Hypothetical performance is not necessarily indicative of future results. No representation is being made that any action will achieve profits or losses similar to those displayed. The result may be overstated as neither transaction costs nor bid/ask spreads nor slippage have been considered. Output equally weighted with maximum 5% allocation per position and rebalanced monthly. Holdings are systematically replaced when the screening criteria are not met anymore. No additional buying or selling rules (technical analysis) have been employed.

# Maximum Drawdown

Is the peak-to-valley decline (usually quoted as a percentage) of an investment during a specific holding period. A drawdown is measured from the time a retrenchment begins to when a new high is reached. This method is used because a valley can't be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the smallest trough is recorded. Drawdowns can help to determine an investment's financial loss risk by looking into the past. # Calculations based on back-tested hypothetical performance since Jan 2000

Original formula

Original formula plus meetinvest positive price momentum rule

Data source: Bloomberg, Calculations: meetinvest

Disclaimer

Hypothetical performance is not necessarily indicative of future results. No representation is being made that any action will achieve profits or losses similar to those displayed. The result may be overstated as neither transaction costs nor bid/ask spreads nor slippage have been considered. Output equally weighted with maximum 5% allocation per position and rebalanced monthly. Holdings are systematically replaced when the screening criteria are not met anymore. No additional buying or selling rules (technical analysis) have been employed.

# Sharpe Ratio

The Sharpe Ratio an indicator whether a portfolio's returns are due to smart investment decisions (meaning better stock picks) or a result of just excess risk. The greater a portfolio's Sharpe Ratio, the better its risk-adjusted performance has been.

It was developed in 1966 by Nobel laureate William F. Sharpe to measure risk-adjusted performance and is calculated by subtracting the risk-free rate from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.

The formula for the forward-looking (ex-ante) Sharpe ratio is:

S_{\text{Sha}} = \frac{E[R_a - R_f]}{\sigma} = \frac{E[R_a - R_f]}{\sqrt{\text{var}[R_a - R_f]}}

Where R_a is the asset return, R_f is the return on a benchmark asset, such as the risk free rate of return or an index such as the S&P 500. E[R_a - R_f] is the expected value of the excess of the asset return over the benchmark return. \sigma is the standard deviation of this excess return.

The formula for the backward-looking (ex-post) Sharpe ratio is the same as for the ex-ante Sharpe ratio, where the expected excess return is replaced by the realized excess return.

# Calculations based on back-tested hypothetical performance since Jan 2000

Original formula

Original formula plus meetinvest positive price momentum rule

Data source: Bloomberg, Calculations: meetinvest

Disclaimer

Hypothetical performance is not necessarily indicative of future results. No representation is being made that any action will achieve profits or losses similar to those displayed. The result may be overstated as neither transaction costs nor bid/ask spreads nor slippage have been considered. Output equally weighted with maximum 5% allocation per position and rebalanced monthly. Holdings are systematically replaced when the screening criteria are not met anymore. No additional buying or selling rules (technical analysis) have been employed.

# Sortino Ratio

The Sortino Ratio is a modification of the Sharpe ratio that only considers the downside (or harmful) standard deviation and was named after Frank A. Sortino. Similar to the Sharpe ratio, the greater a portfolio’s Sortino Ratio, the lower the probability of a large loss.

S_{\text{Sor}} = \frac{E[R_a - R_f]}{\sigma_{-}} = \frac{E[R_a - R_f]}{\sqrt{\text{var}[R_a - R_f]1_{\{ R_a \leq R_f\}}}}

R_a denotes the asset return, R_f the return on a benchmark asset and E[R_a - R_f] the expected (realized) excess return. \sigma_{-} is the semi-deviation (standard deviation of the downside moves only) of the excess return and 1_{\{ R_a \leq R_f\}} denotes the following indicator function:

1_{\{R_a \leq R_f\}} = \begin{cases}1 & \text{if } R_a \leq R_f\\ 0 & \text{else}\end{cases}

# Calculations based on back-tested hypothetical performance since Jan 2000

Original formula

Original formula plus meetinvest positive price momentum rule

Data source: Bloomberg, Calculations: meetinvest

Disclaimer

Hypothetical performance is not necessarily indicative of future results. No representation is being made that any action will achieve profits or losses similar to those displayed. The result may be overstated as neither transaction costs nor bid/ask spreads nor slippage have been considered. Output equally weighted with maximum 5% allocation per position and rebalanced monthly. Holdings are systematically replaced when the screening criteria are not met anymore. No additional buying or selling rules (technical analysis) have been employed.

# Standard deviation

Is the most common statistical measurement that sheds light on historical price fluctuations. It is also known as volatility. A volatile stock such as a young anti-cancer biotech company will have a much higher standard deviation than a stable blue chip stock like the food giant Nestlé. To achieve your expected return with less volatility, you should use a guru strategy with low standard deviation.

The standard deviation measures the dispersion from the mean (average). For a stock with a low standard deviation the price data tends to be very close to the mean, whereas for a stock with high standard deviation the price data is spread out over a large range of values.

The formula is:

\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^N(x_i - \mu)^2}

Where xi is the actual rate of return, μ is the average rate of return and N is the number of time periods.

# Calculations based on back-tested hypothetical performance since Jan 2000

Original formula

Original formula plus meetinvest positive price momentum rule

Data source: Bloomberg, Calculations: meetinvest

Disclaimer

Hypothetical performance is not necessarily indicative of future results. No representation is being made that any action will achieve profits or losses similar to those displayed. The result may be overstated as neither transaction costs nor bid/ask spreads nor slippage have been considered. Output equally weighted with maximum 5% allocation per position and rebalanced monthly. Holdings are systematically replaced when the screening criteria are not met anymore. No additional buying or selling rules (technical analysis) have been employed.

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