Many of the articles that you read online will focus on the 'return' side of the risk-return relationship. In this article I aim to look at the Risk side of the equation and how we can calculate risk metrics that are suitable for a retail investor's time horizon. Moreover, I will look at using the portfolio Beta and volatility to interpret a portfolio's vulnerability to market changes. To make things simpler to understand I will use a sample portfolio with a combination of 5 stocks and exchange traded funds.

I believe that an efficient risk management process is an optimized combination of

- Volatility of Individual Position
- Conviction of Position
- Correlated Volatility which is the Beta with respect to the market

Hence if the Risk Management process overrides individual conviction to reduce relative position size then it compromises on possible return and hence is not an efficient system. On the other hand if the conviction and sheer determination for a position exceeds the risk managed weight allotted for the position then we expose our portfolios to unnecessary capital drawdown. This philosophy leads us to the following system which outlines a logical flow that optimizes conviction and volatility.

__Individual Volatility__

The historical volatility of a stock represents the variance of returns from the mean. In other words it dictates how much volatile daily price movement is. As an example we can see that in the screen shot below (AAPL) has a 36% volatility for the last 50 day period which is calculated using daily returns with standard deviation measured over the last 50 trading days. This implies that the returns have a variance of 36% over a one year horizon if annualized

Volatility is calculated using the Standard deviation of daily return from the last 50 days in the above example and is annualized by multiplying it with square root of T:

Ơ_{T} = Ơ √ T

Where T is 256 (total trading days)

In our sample portfolio below I have taken the time period for historical volatility as 50 days assuming a 2 month investment horizon. However, an alternate method could be to average out short term volatility against longer term volatility using defined weights for both according to investor risk averseness and time period of investment. Investors with longer investment time period horizons would give greater weight to longer term volatility and lesser to short term volatility.

*(click to enlarge)*

Source: barchart.com

__Position Conviction__

The second step involves correctly sizing portfolio positions in order to quantify individual position convictions. When an equally weighted portfolio is configured we assume that the risk taken across each position accurately takes into account the upside potential that is expected from that position (conviction). In reality this is hardly the case since conviction across positions can be variable and hence a system to quantify conviction is needed so that appropriate risk in terms of sizing can be incorporated into the system. The method used in the example below quantifies position size conviction on a scale from 0-1 and hence positions with greatest conviction are 1 and positions with lowest conviction are 0.

__Portfolio Allocation__

Volatility | 1 Trade Unit | Conviction | Weight | Dollar value | |

FB | 51% | 2.4% | 1 | 2.4% | 235 |

MSFT | 21% | 5.7% | 0.75 | 4.3% | 429 |

GS | 22% | 5.5% | 0.5 | 2.7% | 273 |

DIA | 11% | 11.2% | 1 | 11.2% | 1121 |

JNK | 4% | 30.0% | 0.5 | 15.0% | 1500 |

HYG | 5% | 24.0% | 0.5 | 12.0% | 1200 |

1 Trade unit | 10% | ||||

SPY Vol. | 12% | ||||

Dollar Value | 10000 | ||||

Cash | 5242 |

Once individual volatilities and portfolio convictions have been calculated, we determine trade units for every position. A trade unit is a standardized system to harmonize instrument volatility using a market instrument as the base. In the example below we use the (SPY) SPDR exchange traded fund as a market representation. Secondly, we have taken a standard 1 trade unit position as 10% of portfolio invested which can be however be adjusted with respect to total positions in portfolio and cash requirements.

In the table above the first column represents annualized volatility for every position as described before. The 1 trade unit for every position is calculated by dividing the volatility of each instrument by the volatility of SPY and multiplying with standard trade unit size which is 10%. Hence for (FB) the calculation is as follows:

FB trade unit: 12% / 51% X 10% = 2.4%

This implies that if an instrument has the same volatility as the market index then we will take a standard (10%) position in the instrument and if the volatility of the instrument is less than that of the market then the position allocated will be more than 10%.

The final step involves determining position size which is a multiple of our conviction and respective trade units calculated earlier. These allocations are multiplied by the total portfolio dollar value to determine the dollar amount allocated to individual positions as shown in the last column

__Portfolio Beta__

The volatility measure takes into account only individual position risk. However, in order to take into account internal portfolio correlations (positions moving together) we need to calculate a portfolio Beta which is a concept of correlated volatility. Hence a Beta of 1.38 for (GS) implies that for every 1% move in the market, GS moves 1.38% on average which might increase if the correlation with the market improves or overall volatility of the stock increases.

The table below shows the calculation for Portfolio Beta (taking into account that cash has a beta of zero) which is calculated simply by multiplying weights with individual Betas and a summation of weighted Beta to find out Portfolio Beta. Since the individual volatility of a position does not take into account correlations with the market, it is important to actively manage overall portfolio Beta in order to monitor the risk of drawdown of capital due to market correlations.

Weight | Beta | Weighted Beta | |

FB | 2.4% | 1.75 | 0.04 |

MSFT | 4.3% | 0.97 | 0.04 |

GS | 2.7% | 1.38 | 0.04 |

DIA | 11.2% | 0.88 | 0.10 |

JNK | 15.0% | 0.75 | 0.11 |

HYG | 12.0% | 0.64 | 0.08 |

Portfolio Beta | 0.41 |

__Final Note__

The key to an effective risk managed portfolio is finding a balance between the conviction level on a position and the risk taken which is a combination of its correlation with the market and individual volatility. Under an ideal scenario, investors would allocate highly to a position with greater conviction and reducing position size as the correlation with market increases or individual volatility increases. Hence our arithmetic trade unit metric covers the volatility portion of risk and the portfolio beta concept manages overall portfolio risk to take into account market correlation.

In part 2 of this series we will focus on a portfolio divided into Asset classes to take into account correlations between and within Asset classes and Portfolio Value at Risk VAR.

**Additional disclosure:** "Business relationship disclosure: The article has been written by Dividend Pros's Strategist. Dividend Pros is not receiving compensation for it (other than from Seeking Alpha). Dividend Pros has no business relationship with any company whose stock is mentioned in this article."

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