Human beings have developed numerous ways to evaluate different aspect of life. Like school grades in childhood, manager’s appraisal in jobs, return on equity for shareholders, etc. You name the aspect, I bet there will be a measure associated to evaluate it.

Portfolio return is one such measure or ‘the’ most important measure, to measure a portfolio’s performance. It measures the performance of portfolio manager, or yours if you happen to manage the portfolio by yourself.

Among the many available variant for portfolio return below three are most commonly used variants

- Simple Rate of Return (SRR)
- Money Weighted Return (MWR)
- Time Weighted Return (TWR)

Let us understand the difference between these three measures:-

**Simple Rate of Return** - As the name implies it is the most simple way to calculate portfolio return. It is simply return of the current holdings in the portfolio. But unfortunately it is not correct measure of the portfolio return as it does not take into account the performance of past holdings in the portfolio. Most brokerages only provide the return of the current holdings in the portfolio which is not the true return of the portfolio.

**Money Weighted Return** – MWR or IRR (Internal Rate of Return) takes into account the portfolio cash flows for return calculation. It is the return which equates the external cash flows and the ending value of the portfolio with the initial investment made into the portfolio. However, this return is affected by the size and the timing of the cash flows and is not the recommended way for measuring portfolio’s return.

**Time Weighted Return** - TWR is considered to be the true measure of the portfolio return. It calculates the portfolio return after eliminating the impact of cash flows from the portfolio. TWR actually measures the performance of the underlying assets in the portfolio. TWR is recommended by the **Global Investment Performance Standard (GIPS)** for measuring portfolio’s performance. This return can be used for goal setting and comparing the performance of the portfolio with different benchmarks.

**TWR Calculation**

Basic fundamental behind TWR calculation is to break down the holding period into smaller periods such that each period’s start date and end date correspond to any cash flow that occurred in the portfolio. Then the return for each sub period is calculated by eliminating the effect of cash flow from the portfolio’s ending value for that period. After that the returns of each sub periods are multiplied to come up with the true holding period return for the portfolio.

Lets try to understand TWR calculation using a sample portfolio.

**Step 1. Lets start by adding some transactions in the portfolio**

Table 1. Transaction Table

Date | Stock | Qty | Price | Transaction Type |

10-Jan-2013 | Stock A | 10 | 100 | Buy |

14-Apr-2013 | Stock B | 20 | 200 | Buy |

14-Apr-2013 | Stock A | 5 | 120 | Sell |

31-Jul-2013 | Stock B | 10 | 150 | Sell |

31-Jul-2013 | Stock A | 5 | 140 | Sell |

**Step 2. Now using above transactions we will create the portfolio valuation table.**

Create portfolio valuation for each date on which there was a transaction in the portfolio.

Table 2. Valuation Table

Date | Beginning Value | Buy | Sell | Ending Value |

10-Jan-2013 | 0 | 1000 | 0 | 1000 |

14-Apr-2013 | 1200 | 4000 | 600 | 4600 |

31-Jul-2103 | 3700 | 0 | 2200 | 1500 |

Note - For simplicity I have assumed same beginning and ending price on any given day

Sample Calculation –

Beginning Value on 14-Apr = Portfolio holdings at the beginning of 14th Apr * Price

= 10 (Stock A) * 120 (Price of A) = 1200

Ending Value on 14-Apr = Portfolio holdings at the end of 14th Apr * Price

= 5 (Stock A) * 120 (Price of A) + 20 (Stock B * 200) = 4600

**Step 3. Calculate return for sub periods by eliminating the effect of cash flows**

Table 3. Sub Period Return

Period | Beginning Value (Last period’s Ending Value) | Adjusted Ending Value (Ending Value + Sell – Buy) | Return (Using Adjusted Ending Value and Beginning Value) |

10-Jan to 14-Apr | 1000 | 1200 | 20 |

14-Apr to 31-Jul | 4600 | 3700 | -20 |

**Step 4. Compute total time weighted return by multiplying sub period holding period returns**

**TWR = (1 + .2) * (1 – .2) – 1 = – 4%** |

So the total time weighted return for portfolio comes out to be – 4%

**Annualized Return – **We can apply the above approach to calculate the annualized return for the portfolio as well. For e.g lets say the TWR for a portfolio with holding period of 3 years comes out to be 40%. Then we can use the compounding return formula to calculate the annualized return. Therefore, if ‘r’ is the annualized return for each year, then

((1 + r) ^ 3 – 1) = 40

therefore, r = 12% approximately

In next post I will show how we can further improve portfolio return by daily valuing the portfolio. This would also help in measuring the volatility of the portfolio and thus help in comparing the performance of the portfolio with the benchmark as well as other portfolios.