NxMCR - Calculate the Up/Down Market Capture Ratio

Returns the upside and downside market capture ratio (MCR).

Syntax

NxMCR(X,Index,Freq,Down)

X

is the portfolio simple rate of returns data series (a one-dimensional array of cells (e.g., rows or columns)). 

Index

is the index/benchmark simple returns data (a one-dimensional array of cells (e.g., rows or columns)).

Freq

is the data sampling frequency per year (i.e., number of data points in one year) (e.g., 12 = monthly, 4 = quarterly, etc.). If missing, a monthly frequency is assumed.

Down

is an integer switch to select the MCR type: (0 = Upside MCR (default), 1 = Downside MCR).

Value	Description
0	Up-market capture ratio (default)
1	Down-market capture ratio.

Remarks

1. The up-market capture ratio measures an investment manager's overall performance in up/bull markets. It is used to evaluate how well an investment manager performed relative to an index during periods when that index has risen.
2. The up-market capture ratio is calculated by dividing the manager's returns by the index's returns during the up-market.
3. The up-market capture ratio is calculated as follows: $$\textrm{Up-MCR} = \frac{\underset{\forall i, r_i^b>0}{\textrm{CAGR}(r^m)}}{\underset{\forall i, r_i^b>0}{\textrm{CAGR}(r^b)}} $$ Where:
   • $r^b$ is the index or benchmark simple return.
   • $r^m$ is the portfolio or strategy simple return data set.
   • $\forall i, r_i^b>0$ designates the periods in the data set where the benchmark was up (bull).
4. The down-market capture ratio measures an investment manager's overall performance in down/bear markets. It is used to evaluate how well an investment manager performed relative to an index during periods when it dropped.
5. The down-market capture ratio is calculated as follows: $$\textrm{Down-MCR} = \frac{\underset{\forall i, r_i^b<0}{\textrm{CAGR}(r^m)}}{\underset{\forall i, r_i^b<0}{\textrm{CAGR}(r^b)}} $$ Where:
   • $r^b$ is the index or benchmark simple return.
   • $r^m$ is the portfolio or strategy simple return data set.
   • $\forall i, r_i^b<0$ designates the periods in the data set where the benchmark was down (bear).

Examples

Example 1:

Related Links

• Wikipedia - Compound annual growth rate
• Investopedia - Up-Market Capture Ratio
• Investopedia - Down-Market Capture Ratio

References

• Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740