## Market Risk Metrics – Holding Period Return

*in*ICAAP

The Holding Period Return represents the return earned by an instrument (e.g. an equity stock) over the time that it is held by an entity or alternatively over the period of analysis. A positive return indicates that the value of the instrument has grown in excess of its principal amount (i.e. the price or value of the instrument at the beginning of the analysis period). A negative return indicates that the decline in the value has eaten into the instrument’s principal value.

The data used in the calculation includes the starting date of the period to be analyzed, the ending date of the period to be analyzed or the number of days in the window length or study period, the initial price of the instrument on the start date of the analysis and the final price of the instrument on the end date of the analysis.

For example we are asked to calculate the holding period return for stock ABC over the 29 day window length from Starting Date of 1^{st} January 2009 to Ending Date 30^{th} January 2009. On 1^{st} January 2009 the price of ABC stock was 43.82 and on the 30^{th} January 2009 the stock price was 42.41

The holding period return is given by the following formula:

For our example this means:

Holding Period Return for Stock ABC = Stock Price on 30^{th} January 2009/ Stock Price on 1^{st} January 2009 -1 = 42.41/43.82-1 = -0.0322 or -3.22%.

This means the value of ABC stock on 30^{th} January 2009 has declined by 3.22% from its value on the 1^{st} of January 2009

The holding period return is also used in the calculation of the Sharpe and Treynor ratios which will be discussed in later posts related to the Portfolio Risk Metrics course. These ratios are annualized measures. Therefore, the holding period return calculated also needs to be scaled to an annual period. For this scaling we need two additional inputs. Firstly we need to know the number of trading days in the year. For example purposes let us assume that there are 252 trading days in the year. Secondly we need to determine the number of trading days in the period of analysis. For our example, this amounts to determining the number of days that the stock traded between 1^{st} January 2009 to 30^{th} January 2009 (start and end dates inclusive). Let us assume that this works out to 20 days.

The scaled holding period return, i.e. annualized holding period return is:

Scaled Holding Period Return = Holding Period Return × Number of trading days in the year/ Number of trading days in the analysis period

Scaled holding period return for Stock ABC = -3.22% × 252/20 = -40.59%.

Let us now consider another example:

Calculate the Scaled Holding Period Return for Stock XYZ for the period 1-Jan-2009 to 31-Mar-2011. The stock prices on these dates were 12.20 and 14.10 respectively. The number of trading days in a year is assumed to be 252 days whereas the stock had traded for a total of 563 days during the analysis period.

The un-scaled holding period return for Stock XYZ works out to:

Holding period return for Stock XYZ = Stock Price on 31^{st} March 2011/ Stock Price on 1^{st} January 2009 -1 = 14.10/12.20-1 = 0.1557 or 15.57%.

The scaled holding period return, i.e. the annualized return for Stock XYZ works out to:

Scaled holding period return for Stock XYZ = 15.57% * 252/563 = 6.97%.