# Calculating Discrete Holding Period Returns

### Abdulla Javeri

30 years: Financial markets trader

As investors or traders, the main objective is to make a profit. Returns can be calculated for a holding period or on an annualised basis, and on a continuously compounded basis or a discrete basis. In this video, Abdulla will provide a formula for calculating returns on a discrete basis for both the holding period and an annual percentage return.

As investors or traders, the main objective is to make a profit. Returns can be calculated for a holding period or on an annualised basis, and on a continuously compounded basis or a discrete basis. In this video, Abdulla will provide a formula for calculating returns on a discrete basis for both the holding period and an annual percentage return.

### Calculating Discrete Holding Period Returns

4 mins 37 secs

Key learning objectives:

Describe the basic properties of calculating returns

Identify the relevant formulae for calculating holding period returns and annualised returns

Overview:

Calculating returns can be expressed as a percentage gain or loss on an investment. Investors main objective is to make a profit - a positive return on their investment. These returns can be calculated using the formulae outlined below.

#### What are some of the basic properties of calculating returns?

- Expressed as a percentage gain or loss on an investment
- Can be calculated for the holding period, or, on an annualised basis
- Can be expressed as a discrete return, or, on a continuously compounded basis

#### How do we calculate holding period returns?

**Holding Period Return** = Sell price / Buy price - 1

Or

**Holding Period Return** = (Sell price - Buy price) / Buy price

For a price series

**Holding Period Return** = End value / Start value - 1

- The holding period return is simply the selling price divided by the buying price minus 1.
- Or, looking at the middle formula, it’s the profit as a percentage of the cost.
- If you currently hold an investment and you want to calculate the periodic returns since you made the investment, simply take a price (end value), divided by the previous price (start value) and subtract 1.

#### Using the information below, how do we calculate the holding period for both investors?

- Investor A - has made $100,000 in one year
- Investor B - has made $50,000 in six months

- The holding period for Investor A is 10%, 100,000/1,000,000
- The holding period for Investor B is 50%, 50,000/100,000

Investor B has a greater return in a shorter time, and thus has clearly done better.

#### How do we calculate annualised returns?

If the holding period is less than a year, we use the top formulae. And if the holding period is greater than a year, we use the bottom one.

**Annual Return** = Holding period return x 365 / holding period (days)

Or

**Annual Return** = (Sell price / Buy price)^{(1/years held) - 1}

(Multi-period TVM formula re-arranged to solve for r)

#### For the following examples, what is the holding period return and annual return?

**Question 1:**

- Buy Price = 250
- Sell Price = 265
- Holding Period = 30 days

- Holding period return: (265/250) - 1 =
**6%** - Annual return: (6 x 365)/30 =
**73%**

**Question 2:**

- You bought shares 10 years ago for 150, and you sold them for 650.

- Holding period return: (650/150) - 1 =
**333.3%** - Annualised return - As the holding period is greater than one year, we do the following calculation: (650/150)
^{(1/10) - 1}=**15.79%**

### Abdulla Javeri

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