Percentage rates appear to be popular in many financial publications. We see them in different forms- either positive or negative. As investors, some common areas we find percentage rates interesting are documents that deal with investment returns or profits. Many investors, as well as prospective ones, look out for rates quoted by financial institutions to make informed decisions. Unfortunately, most prospective investors get confused in the interpretation of these rates. Besides the misinterpretation of percentage rates, others naively compare rates associated with different investment categories. Their naivety reflects in the manner they query or make statements such as:

- “Which mutual funds have the highest interest rates?”
- “Which stocks have high interest rates?”
- “The interest rate of Mfund [money market fund] is higher than that of Epack [equity fund]”

One consequence of misinterpreting percentage rates is the disappointment that follows when lower-than-expected returns are made on an investment. During a chat with John (a follower of Sikasεm) a few days ago, I was not surprised when he expressed the frustration he had recently been through. He revealed:

*“I nearly cried when 700 cedis in an account yielded only 4.57cedis.”- John Mensah*

I understand many more people have had such an experience before. Yes! It is a very painful experience to go through. However, to avoid or reduce the impact of similar painful experiences, it would be worthy to study a few of the percentage rates we usually come across in investment products.

### Annual interest rate

The most common investment products that make use of **annual interest rates** are Treasury bills and fixed deposits. The interest rates quoted on the various Treasury bills and fixed deposits are annually-based. That is, the return or profit earned on these investment products, when utilising the quoted interest rates, is for a period of one year (12 months). However, T-bill investments do not always mature in 12 months. For instance, the **91-day** and **182-day** T-bills mature after **three months** and **six months** respectively. Hence, the calculated interests need to be prorated (distributed) for the actual maturity periods. That is three months and six months for the 91-day and 182-day T-bills respectively.

To be clearer on this, let’s go through the sample calculation below.

** **How to calculate Treasury bill interest

Let’s assume that you invest GH¢1000 at the current **91-day** T-bill rate of **13.4700%**,

Now, since the quoted interest rate (**13.4700%**) is an annual (12-month) rate, the total interest on the GH¢1000, after 12-months, would have been **(1000×0.1347) = GH¢134.7 **

However, **91-day** T-bill investment matures after three months. Hence the above total interest needs to be prorated for a **three-month** investment period.

Thus, the real interest to be earned on the GH¢1000 would be **(1000×0.1347)/4 = GH¢33.675**

Note that **3 months × 4 = 1 year**. That is why you see the total (annual) interest being divided by 4

In a similar manner, the annual interest would have been divided by **2** if it were to be **182-day** (6 months) T-bill investment.

Another means to estimate your T-bill or fixed deposit interest is to first distribute the calculated annual interest **per each month** and further multiply the monthly interest by the actual number of months the money stayed invested. Using the same example above, the interest earned per month would be **(1000×0.1347)/12 = GH¢11.225 **Remember that there are 12 months per annum (year).

Now, since the money is being invested for 3 months (**91-day** T-bill), we multiply the monthly interest figure by 3. That is, (**GH¢11.225×3) = GH¢33.675**

** **

### Annual yield

**Annual yield** is the annual rate of return on an investment, taking into consideration the compounding effect of any intermediary interest earned. **Annual yield** is most often reported as the investment return on money market funds (a pool of fund invested in fixed income products). Managers of money market funds, while estimating the **annual yield**, assume that the funds would remain intact in the account for one year (365 days). For instance, the estimated annual yield of **HFC Unit Trust** on 10th May 2017 was reported as **20.31%**. What this means is that assuming the funds in **HFC Unit Trust** remain intact from 10th May 2017 to 10th May 2018 (one year), the estimated rate of return would be **20.31%**. That is, the value of the mutual fund would appreciate by **20.31%**. However, since investors continue to deposit and withdraw from mutual funds, the funds are therefore not expected to remain intact throughout the full year. Thus, fund managers keep revising their **annual yield** on a daily basis to reflect the changes. For this reason, it may be difficult to precisely calculate the return on a mutual fund (money market) investment over a period.

Due to the effect of compounding, investment returns associated with money market funds may not be evenly distributed over the investment duration. Let’s assume that you had invested GH¢1000 in Databank’s Mfund on 12th May 2017. **Annual yield** of Mfund on 12th May 2017 was **19.88%**. Thus, the estimated return (profit) on the GH¢1000 after one year would be **(GH¢1000×0.1988) = GH¢198.8 **However, the **GH¢198.8 **takes into account the compounding effects of intermediary profits that are reinvested by the fund managers. As such, it cannot be equally distributed by each of the 12 months. This implies that if the GH¢1000 stays invested for just six months instead of the 12 months, you cannot expect to earn half of the annual profit.

Once again, let’s go through another example using real historical data.

**Table: Historical investment value of an Mfund account**

**Date** |
**Mfund value, ****GH¢** |
**Monthly return,**** GH¢** |

30/09/2016 |
879.41 |
—– |

31/10/2016 |
894.71 |
15.3 |

30/11/2016 |
912.03 |
17.32 |

31/12/2016 |
928.61 |
16.58 |

31/01/2017 |
945.83 |
17.22 |

28/02/2017 |
958.98 |
13.15 |

31/03/2017 |
971.49 |
12.51 |

30/04/2017 |
988.82 |
17.33 |

The table above shows the value of an Mfund investment account (a money market fund) over a seven-month period. Based on the investment values, the monthly returns are also calculated by subtracting preceding values from current ones.

Even though the fund manager (Databank) had estimated an **annual yield** of about 23% at the time, the returns (as seen in the table) were not equally distributed over the period- They differed from one month to another. For instance, November return of **GH¢****17.32 **had increased from the October return of **GH¢****15.3**. On the other hand, the return in January (**GH¢****17.22**) had dropped to **GH¢****13.15** in February. Factors that account for non-equal distribution of Mfund returns include, but not limited to, compounding effect of intermediary profits as well as changes in interest rates of fixed income products during the investment period.

### Year to date return (YTD)

Whenever we mention year to date, we refer to the period between the start of a calendar year and the present date of the same year. The beginning of the calendar year often has 1st January as the baseline. **Year to date return** therefore refers to the return or profit made so far, from 1st January to the present day of the calendar year. For instance, a **year to date** investment return of 10%, as of 30th April 2017, implies that from 1st January to 30th April 2017, a return of 10% had been made on the investment.

Year to date returns are usually reported on equity-related investment products such as the Ghana Stock Exchange (GSE), Epack investment fund, SAS fortune fund and HFC Equity Trust. Similar to the annual yield explained earlier, **year to date returns** can drop or increase from time to time within a calendar year. Again, **year to date returns **do not accumulate in a linear functional manner. In other words, they do not distribute proportionally along the calendar year. The mere fact that a **year to date return** after the first four months (30th April) was 10% does not necessarily mean that the return at the end of the year (31st December) would be 30%. This is due to price fluctuations on the equity markets. On every business day, equity fund managers recalculate their **year to date returns** based on the present prices of stocks.

It is also important to note that published **YTD returns** mostly affect existing shareholders than prospective ones. Now let’s have a look at the scenario below:

From the scenario above, it is clear that the investor lacked understanding of **YTD returns**. This is a common mistake many prospective investors make when investing in equity funds. As I mentioned before, **YTD returns** mostly affect existing shareholders. Thus, the 45% the prospective investor noticed in September 2016 was a profit that had been ‘earned’ already by the existing shareholders of the equity fund. To accurately estimate his return, he needed to do that in reference to September 2016 since that was when he made the deposit. According to the scenario, the fund had lost 5% (45% to 40%) from September to December. Hence, the investor had actually lost part of his deposit.

In a similar situation, an existing shareholder who topped up his account in September 2016 would not enjoy profit on the additional deposit that was made in September. Nevertheless, he would enjoy the 40% return on his previous investment (prior to the deposit in September) if that investment had stayed in the equity fund from January to December 2016.

### Comparing percentage rates

It is important not to compare percentage rates of different categorical investments. For example, the **annual yield** of HFC unit trust (a money market fund) as of 10th May 2017 was **20.31%**. On the same day, the **year to date return **on HFC equity trust (an equity mutual fund) was **9.68%**. It would be a big mistake to compare these two percentage rates and assume that HFC unit trust performs better than HFC equity trust. This is because the 9.68% return on HFC equity trust is only for the period of 1st January 2017 to 10th May 2017 while the 20.31% on HFC unit trust is a 12-month estimated rate.

On another note, it may not be appropriate to compare the year to date (YTD) returns of two different equity funds in the early part of a year. As stated earlier, **YTD returns** do not distribute proportionally along the calendar year. For instance, the **YTD returns** of SAS fortune fund and Epack investment fund, as of 11th May 2017, were 14.51% and 5.4% respectively. While the rate for SAS fortune fund is higher than that of Epack, it may be premature to conclude that SAS fortune fund performs better than Epack investment fund. This is because the **YTD return** of SAS fortune fund may drop while that of Epack can rise steeply before the year ends. Thus, a more appropriate comparison could be done at the end of the calendar year.