# Portfolio Management

Track your trades and calculate the risk, using an excel document.

Risk Management

Risk management is a crucial process used to make investment decisions. Risk management involves identifying and analyzing risk in an investment and deciding whether or not to accept that risk given the expected returns for the investment.

Why Is Risk Management Important?

Risk management—specific to investing—is important because it evaluates potential upsides and downsides to securities. Instead of solely focusing on the projected returns of an investment, it considers the potential loss of capital and informs the investor of the unfavorable outcomes that may occur with an investment.

What Are the 2 Major Types of Risk?

The two major types of risk are systematic risk and unsystematic risk. Systematic risk impacts everything. It is the general, broad risk assumed when investing. Unsystematic risk is more specific to a company, industry, or sector. You're stuck with systematic risk, but you have complete control over how much unsystematic risk you want to carry.

What Is Value at Risk (VaR)?

Value at risk (VaR) is a statistic that quantifies the extent of possible financial losses within a firm, portfolio, or position over a specific time frame. This metric is most commonly used by investment and commercial banks to determine the extent and probabilities of potential losses in their institutional portfolios.

Risk managers use VaR to measure and control the level of risk exposure. One can apply VaR calculations to specific positions or whole portfolios or use them to measure firm-wide risk exposure.

VaR Methodologies

There are three main ways of computing VaR: the historical method, the variance-covariance method, and the Monte Carlo method.

Historical Method

The historical method looks at one’s prior returns history and orders them from worst losses to greatest gains—following from the premise that past returns experience will inform future outcomes. See “Value at Risk (VaR) Example” below for the formula and how it’s calculated.

Variance-Covariance Method

Rather than assuming that the past will inform the future, the variance-covariance method, also called the parametric method, instead assumes that gains and losses are normally distributed. This way, potential losses can be framed in terms of standard deviation events from the mean.

The variance-covariance method works best for risk measurement in which the distributions are known and reliably estimated. It is less reliable if the sample size is very small.

There is also a precise closed-form solution involving the inverse Mills ratio.

Monte Carlo Method

A third approach to VaR is to conduct a Monte Carlo simulation. This technique uses computational models to simulate projected returns over hundreds or thousands of possible iterations. Then, it takes the chances that a loss will occur—say, 5% of the time—and reveals the impact.

The Monte Carlo method can be used with a wide range of risk measurement problems and relies upon the assumption that the probability distribution for risk factors is known.

Modified VaR

Modified value-at-risk allows to estimate losses for return distributions that are non-normal, penalising negative skewness and positive kurtosis.

VaR Backtest

In recent years many concepts for managing and measuring risk have developed. The main methodology for managing risk is a method of value at risk, which, in practice, is combined with other techniques for minimizing risks, in order to achieve optimal business results. Value at risk (VaR) is the biggest loss of the portfolio that can be expected in the reporting period, with a given level of confidence. This value is a simple, easily understandable number that presents the risk which the institution is exposed to on financial market. The principle of calculating capital is based on the VaR methodology. However, backtesting of calculated VaR amount is needed. Backtesting is the process where the real gains and losses are compared to the forecasted VaR estimates.

Kupiec POF Method

Kupiec (1995) introduced a variation on the binomial test called the proportion of failures (POF) test. The POF test works with the binomial distribution approach. In addition, it uses a likelihood ratio to test whether the probability of exceptions is synchronized with the probability p implied by the VaR confidence level. If the data suggests that the probability of exceptions is different than p, the VaR model is rejected.

# Portfolio Performance

R-score

R-score is a ratio that measures the wins against the losses.

Distribution of returns

Evaluation of the wins and losses. It shows if the risk management is good or not. Good portfolio should have good wins and controlled losses.

True value of the portfolio

Excluded deposits and withdrawals.

Portfolio index represent the true returns of the portfolio.

Historical statistic

Mean - an average return

Sigma – standard deviation of all returns. Used as a risk of the portfolio

Downside Sigma – standard deviation of losses. This measurement is more important for the portfolio manger, because he is concern to control more the losses than the wins.

Mode - The mode is the value that appears most frequently in a data set.

Kelly Criterion

Kelly criterion works on the principle of maximize the profit in a given known inputs, meaning the amount and loss of every trade is known and the profit is guaranteed. Also the percentage of wins and losses are also known and guaranteed. In the reality the inputs are unknown and the wins are not guaranteed.

It is very important to understand that Kelly criterium is to maximize the profits and has no consideration of the risk. As we know profit and loss are increasing linearly.

Full Kelly – Kelly criterium is better to be used as an indicator of portfolio performance rather than position sizing. Higher Kelly indicate better performance.

Betting Kelly - Betting Kelly criterium is adjusted to the losses and can be used as a guide of position sizing in order to maximize the profit. It is a recommendation for the absolute limit of the position size.

Gross Sharpe Ratio

The Sharpe ratio normalizes absolute returns for a given level of risk.

Values:

Negative values – means that the portfolio has negative returns

0-0.5 – poor

0.5-1 – optimal

1-1.5 – good

1.5-2 - very good

Above 2 – excellent

Gross Sortino Ratio

The Sortino ratio is a variation of the Sharpe ratio that only factors in downside risk.

Because of the fact that the distribution of returns is not normal, this ratio will give us much better inside of the portfolio than Sharpe ratio.

Values:

Negative values – means that the portfolio has negative returns

0-1 – optimal

1-2 – reasonable

2-3 - good

Above 3 – excellent

Calmar Ratio

The Calmar ratio is a gauge of the performance of investment funds such as hedge funds and commodity trading advisors (CTAs). It is a function of the fund's average compounded annual rate of return versus its maximum drawdown. The higher the Calmar ratio, the better it performed on a risk-adjusted basis during the given time frame, which is mostly commonly set at 36 months.

Values:

Negative values – means that the portfolio has negative returns

0-0.5 – optimal

0.5-1 – reasonable

1-2 - good

Above 2 – very good

Risk Calculator

Based on a given inputs, it calculate the potential risk and position sizing.