The number one reason one invests is to make money. The gains or losses that occurred in investments are the return on investments. While there are many reasons to do this, the main is to decipher whether the investment is feasible. It helps decide if you should reinvest your profits or pull your money out.

There are many ways to calculate the returns on investments, and this article brings you the best five.

**Importance Of Calculating The Returns On Investment**

But before we start, it is important to see why calculating returns is crucial.

- It helps understand how the investment is doing if it is recurring profits or losses.
- It helps measure the competition around the market.

**1. Holding Period Returns (HPR)**

This method of calculating returns is an important metric used in managing investments. The return is received over a period that a financial asset or a portfolio of assets has been held.

**Features**

- It is also called the Holding Period Yield (HPY)
- It has two main components, an income component, and a capital appreciation component.
- This metric is usually expressed as a percentage.

**Formula used: (Income + (End Of Period Value – Initial Value))/Initial Value**

**Benefits**

- This formula is the simplest and quickest to find returns on investment.
- It helps manage risk by considering the asset’s holding period.
- It is handy for comparing different investments held for different time durations.
- It takes into account the gains as well as related distributions. This helps it in giving a comprehensive view of performance.
- It is useful in identifying a suitable tax rate. It does so by calculating returns from the day of acquisition to the day of sale.

**Example**

Arjun invests ₹15,00,000 three years back in some of the real estate stocks that have generated dividends of ₹15,000. He sold it after 10 months and received₹17,50,000.

The Holding Period Return he gets is,

HPR = 15000 + (1750000-1500000)/1500000

= 17.6%

**2. Annualized Holding Period Return**

One drawback of this metric is that it is not a standardized yield measure. Thus, a direct comparison between returns on different investments is not suitable. But finding the total time of the investment and then converting it to annualized HPR is.

**Formula used: Annualized HPR = (1 + HPR) ^{1/n }– 1 **

**Example**

Taarini held the investment for three years. It appreciated from ₹10,000 to ₹14,000 providing ₹500 as dividends.

Shruti held the investment for two years. It appreciated from ₹9,000 to ₹13,000 providing ₹1,000 as dividends.

HPR for Investment by Taarini = 0.45 or 45%

HPR for Investment by Shruti = 0.55 or 55%

According to HPR, investments by Shruti is a better option. But since the time duration is different, it is important to calculate annualized HPR

Annualised HPR for Taarini = (0.45 + 1)^{1/3} – 1 = 13%

Annualised HPR for Shruti = (0.55 + 1)^{1/2} – 1 = 24%

The percentage of returns received has changed when the time duration is a consideration.

**3. Post Tax Returns**

This method calculates actual returns left after paying tax on investments.

**Formula used: ****Post-tax returns = Pre-Tax returns * {(100-Tax Rate) / 100}**

**Benefits**

- More accurate depiction of earnings
- It is the opposite of the nominal rate of interest, which looks at gross returns only.

### Example

Shalini has invested ₹1,00,00 in the stock market. After 3 months, I received a dividend of ₹2,000. She then decided to sell her share for ₹1,45,000. The Holding Period return is 14%

She has to pay a 15% tax.

Post Tax Returns = 14* {(100 – 15) / 1000}

= 11.9 %

Post-tax returns = 14 * {(100-150 / 100}

Post – tax returns = 11.9%

Thus the actual returns received after considering taxes is 11.9%.

**4. Inflated Adjusted Returns**

This formula calculates the actual returns left after taking inflation into account. Inflation is essential to consider, as it reduces the purchasing power of your money.

**Features**

- Also known as Real Rate of Return as it gives a more realistic image of the investment’s performance.
- Applied during the withdrawal phase
- Amount achieved after applying this formula is always less than before

**Formula used: ((1+ Return)/ (1+ Inflation Rate)) – 1**

**Benefits**

- Allows the investor to see real returns without any external economic force
- Useful when comparing investments made in various countries. Every country’s rate of inflation is different. Thus it helps bring it all on one level.

**Example**

Anjali buys a stock for ₹1,000 and sells it for ₹4,000 a year later. Her return is 20%. The inflation rate in her country was 4%.

Inflation-Adjusted Return = [(1+.20)/(1+0.04)]-1

= 15.38%

Thus even though Anjali’s return might look 20%, her inflation-adjusted return is 15.38%.

**4. Compounded Annual Growth Rate**

This is the year-over-year growth rate of any specific investment over some time.

**Features**

- It is also known as annualized returns.
- It compares returns on mutual funds, stocks, etc.
- It does not show any investment risks.
- To compare returns from different investments, the periods must be the same.

**Formula Used: (End Value/Beginning Value) ^{1/Years} – 1**

**Benefits**

- It is a representational figure rather than a true one. It shows the rate at which an investment would grow if the profits are re-invested.
- It makes it easy to understand the returns as it smooths it out. This makes it easy to compare two alternative investments.
- It calculates the average growth of an investment.
- By smoothening out returns, volatile and inconsistent returns are easy to understand.
- It is useful in tracking the performances of businesses alongside one another. This helps track weaknesses and strengths amongst competitors.
- This formula is easy to manipulate to suit each specific investment.

**Examples**

**i.** Ankur invested ₹1,000 in a fund for three years. Its value increased to ₹1,300 in the first year. In the second year, it valued at ₹1,700. Upon maturity, the final value stood at ₹1,900.

CAGR = (1900 /1000)^{1/3} – 1

= 23.85%

Thus the Compound Annual Growth Rate for Ankur’s investment is 23.85%

**ii.** Ria bought a stock at ₹100 in 2017. It appreciated by 25% to be ₹125 in 2018. It further increased to be ₹150 in 2019. Thus the appreciation for Ria’s investment is 50%.

CAGR = (150 / 100)^{1/2} – 1

= 22.47%

Thus the Compound Annual Growth Rate for Ria’s investment is 22.47%.

**5. Effective Annual Rate**

This formula gives the rate of interest on investments by compounding interest over a period of time.

**Features**

- It also is the annual equivalent rate, effective interest rate, and effective rate.
- It can calculate interest with different compounding periods: yearly, quarterly, monthly, weekly, etc.
- It is usually higher than the nominal rate. The nominal rate only gives a yearly percentage while EAR gives it with many.
- EAR increases with time; if the number of compounding periods increases

**Formula Used: Effective Annual Rate = (1 + i/n) ^{n} – 1 **

Where,

**i**= annual interest rate

**n**= number of compounding periods

* To use this formula, it is important to determine the number of compounding periods. The most used are 12 (monthly) and 4 (quarterly). The others used are

Monthly – 12 compounding periods

Quarterly – 4 compounding periods

Bi-weekly- 26 compounding periods

Weekly – 52 compounding periods

Daily – 365 compounding periods

**Benefits**

- It converts a nominal return on investments into an effective annual rate.
- It gives the real percentage of interest owed on any debt like a loan or credit card.

**Examples**

**i.** HDFC bank gives a nominal interest rate of 12% on a deposit to Aakash, a bank client. Aakash asks that the interest compounds monthly over the year.

Effective Annual Rate for Nitin’s investment = (1 + 0.12/12)^{12} – 1

= 12.68%

After looking at compounding, the interest rate becomes 12,68% as opposed to 12%. This means that the money deposited will grow by 126.83 for one year.

**ii.** Nitin pays an interest of 10% on an investment that compounds monthly. Ranjan pays an interest of 10.1% compounded semi-annually.

Effective Annual Rate for Nitin’s investment = (1 + 0.1/12)^{12} – 1

= 10.47%

Effective Annual Rate for Ranjan’s investment = (1 + 0.101/2)^{2} – 1

= 10.36%

Ranjan’s investment has a higher nominal interest rate but a lower effective annual rate. This is because Ranjan’s investment compounds fewer times in the year, 2 as opposed to 12.

**FAQs**

### 1. Can the Holding Period Return be negative?

Yes. Like all other returns on investments, this particular return can be negative. It implied that instead of gaining money, the investor is losing it.

### 2. What is the difference between an expected return and a holding period return?

Returns from the expected return are from a probability-weighted average. Thus it describes a probable return. Whereas holding period return calculates return received over a holding period. Thus, it reflects the assets past performance.

### 3. Which of the two, nominal or inflation-adjusted, is better to calculate returns?

Nominal tools do not take into account taxes, inflation, or even investment fees. Thus, they give a very unrealistic picture. Thus, inflation-adjusted tools are always better and much more realistic.

### 4. Can HPR and CAGR ever be the same?

Yes. If the holding period for an investment is 1 year, then HPR and CAGR are the same.

### 5. If CAGR is less than HPR, what does that imply?

CAGR is less than HPR if the holding period is more than 1 year.

### 6. Is CAGR the best formula, or does it have any limitations?

Like every tool, CAGR, despite being very useful, also has its set of limitations-

i. By smoothening out any volatility, it shows the investor that ii. growth has been steady. Thus, depicting an untrue scenario

It does not account for the risk of any investment.

### 7. Is a higher effective annual rate better?

This formula (EAR) is mostly used to compare different interests offered. Out of two, the one with the higher EAR is a better plan.

### 8. How does one apply all these formulae to calculate the returns?

You can use all five of these formulae on a financial calculator or MS Excel.

**Bottom Line**

These five formulas bring all the information needed to calculate returns on investments. They will help you get your foot into the door with investing and teach you to be smart with your finances.

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