In this article, we cover the holding period return formula (HPR formula) and how to calculate the holding period return for a portfolio of investments. This includes the example and calculation of this return, its interpretation, and analysis as well as advantages and disadvantages of it.
Let’s go through together!
Table of contents
What is Holding Period Return (HPR)?
First, let’s understand the key definition of holding period return (HPR). Holding period return (HPR) refers to the return from holding any investments or portfolios or any securities over a certain period of time in percentage term. This HPR includes both income and capital gain.
Income on a given investment, portfolio, or security is commonly in the form of interest earned or received over a period of time. Basically, we consider the income received as a realized return. However, not all incomes on investment are realized. This is because some other incomes are the accrued interest for tax purposes but is not a realized income until the date of settlement.
On the other hand, capital gain refers to the gain or loss of holding security as a result of the increase or decrease in its value. For example, if an investor bought security at a value of $90 and hold it for 3 years. At the end of year 1, the market value of the security is at $95. Thus, the capital gain is $5 ($95 – $90). This capital gain is considered as realized when the investor sells it out for cash; however, it will become unrealized when the investor keeps holding such security for the next 2 years.
Holding Period Return Formula
So how to calculate the holding period return?
As its name suggests, it is calculated by dividing the total returns with its initial investment cost or beginning the investment value of an investment or portfolio. These total returns consist of both interest income and capital gain.
Therefore, we can summary the holding period return formula as follow:
Holding Period Return = (Inc. + CG)/ Vo
Where:
Inc. = Income during the given period
CG = Capital gain which is the difference between ending investment value and beginning investment value
Vo = Initial investment value or beginning investment value
The formula above can be broken down into income yield and capital gain yield as follow:
Holding Period Return = Income Yield + Capital Gain Yield
Where:
Income Yield = Inc. / Vo
Capital Gain Yield = CG/Vo
Example
ABC Co holds four investment vehicles such as saving account, common stock, bond and real estate.
Below is the extracted data of key financial variable of those four portfolios:
| Saving Account US$ | Common Stock US$ | Bond US$ | Real Estate US$ | |
|---|---|---|---|---|
| Cash Received: | ||||
| 1st quarter | 15 | 10 | 0 | 0 |
| 2nd quarter | 15 | 10 | 70 | 0 |
| 3rd quarter | 15 | 10 | 0 | 0 |
| 4th quarter | 15 | 10 | 70 | 0 |
| Total Income | 60 | 45 | 140 | 0 |
| Investment Value: | ||||
| Ending of Year | 1,000 | 2,200 | 970 | 3,300 |
| Beginning of Year | 1,000 | 2,000 | 1,000 | 3,000 |
| Capital Gain | 0 | 200 | (30) | 300 |
Calculate the holding period return of those four investment vehicles.
Solution
We can calculate the holding period return of those four investment vehicles by using the below formula:
Holding Period Return = (Inc. + CG) / Vo
From the extracted data above, we can calculate the holding period return in tabular as below:
| Saving Account US$ | Common Stock US$ | Bond US$ | Real Estate US$ | |
|---|---|---|---|---|
| Total Income (A) | 60 | 45 | 140 | 0 |
| Capital Gain (B) | 0 | 200 | (30) | 300 |
| Total Return (C = A + B) | 60 | 245 | 110 | 300 |
| Beginning Investment Value (D) | 1,000 | 2,000 | 1,000 | 3,000 |
| Holding Period Return (D = C/D) | 6.00% | 12.25% | 11.00% | 10.00% |
Interpretation and Analysis
The return after holding for one year period for common stock is higher than other investment vehicles. The HPR on the common stock is 12.25% while the least HPR is on saving account which is at 6%. The HPR on bond and real estate is at 11% and 10% respectively. This indicates that only common stock provides the highest HPR.
As you can see, the real estate investment also provides a good return which is totally from capital gain. However, it requires a big investment cost which is 50% higher than the cost of investment on common stock. Generally, the risk of investment in real estate is high as compare to other investment vehicles.
Among the four investment vehicles, only saving account and bond have less risk as compare to common stock and real estate because these investments provide a prioritized payment options if companies being invested face any losses or liquidation.
Annualized Holding Period Return
The above calculation is useful for investment portfolios of the same period. If each portfolio has a different period, an alternative approach that is annualized HPR shall be used. Below is the formula for annualized HPR:
Annualized HPR = [(Inc. + CG) / Vo] 1/n – 1
Or Annualized HPR = (1+HPR) 1/n-1
Example
In order to illustrate the annualized HPR, let’s assume that we have two investment securities. Bond A has maturity of 3 years with initial investment of $970. The coupon rate of Bond A is 10% the same as example above. On the other hand, bond B is a 10% coupon rate bond with a maturity of 5 years. The initial investment of this bond is $950. The par value of the bond is $1,000 which will be redeemed at the end of year 5.
Solution
From the above example, we can calculate the annualized HPR as follow:
Annualized HPR = [(Inc. + CG) / Vo] 1/n– 1
First, let’s calculate the HPR of both bonds.
| Bond A US$ | Bond B US$ | |
|---|---|---|
| Cash Received: | ||
| Year 1 | 50 | 50 |
| Year 2 | 50 | 50 |
| Year 3 | 50 | 50 |
| Year 4 | 0 | 50 |
| Year 5 | 0 | 50 |
| Total Coupon Income (A) | 150 | 250 |
| Investment Value: | ||
| Initial Investment (B) | 970 | 950 |
| At maturity (C) | 1,000 | 1,000 |
| Capital Gain (D = | 30 | 50 |
| Total Returns (E = A + C) | 180 | 300 |
| HPR (F = E/B) | 18.56% | 31.58% |
Therefore, we can calculate the annualized HPR for both bonds as follow:
Annualized HPR – Bond A = (1 +18.56%) 1/3 – 1 = 5.8%
Annualized HPR – Bond B = (1 +31.58%) 1/5 – 1 = 5.6%
From the above calculation, if we look at HPR alone without factoring annualized return, bond B provides the highest return at 31.58% while bond A is only at 18.56%. However, if we look at the annualized return, bond A provides a bit better return which is 5.8% as compare to bond B at 5.6%.
Advantages of Holding Period Return
There are a number of advantages of holding period return as follow:
- Holding period return calculation is easy and straight forward to calculate. Because the return is calculated by dividing the total return against the initial investment, the result is considered as the return per invested dollar. Thus, it is easy to understand.
- This return can be used as an investment decision as it gives a relative percentage that can be compared among several projects or portfolios regardless of different sizes of investments.
- It takes into account both income generated and capital gain. This provides a full picture of the overall return of an investment project or portfolio.
- It provides a logical method for the evaluation and comparison of investment returns of multiple investments; particularly for holding periods of one year or less. This is because it reflects the efficiency of investment from the return per invested dollar.
Disadvantages of Holding Period Return
One of the primary disadvantages of holding period return is it fails to consider the time value of money. The calculation of this return does not take into account the time value of money which is very critical; especially for investments or portfolios of more than one year period.
Therefore, for any investments of more than one years, this return shall not be used as investment decision due to lack of time value of money consideration. Thus, a more present value-based measure for example yield or internal rate of return (IRR) should be used instead.
Conclusion
Holding period return is one of the investment decision tool that is used to evaluate and compare the return of investment portfolios. This return is useful only for portfolios with one year or less. For any portfolios with more than one year periods, this return shall not be used because it ignores the time value of money.
