- CFA Exams
- 2021 CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 11. Discretely and Continuously Compounded Rates of Return

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**CFA Practice Question**

An investment offers a 10% stated annual return. What is the equivalent return if it is continuously compounded?

B. 2.30%

C. 10.52%

A. 2.20%

B. 2.30%

C. 10.52%

Correct Answer: C

If the return is compounded continuously, it will equal e

^{0.1}- 1 = 0.1052, or 10.52%.###
**User Contributed Comments**
19

User |
Comment |
---|---|

danlan |
It should be greater than 10%, so no other choice than C |

mtcfa |
I think this question is absolutely wrong. The continuos rate of return should be 9.53% as demonstrated in the notes. Example: An investment goes from 100 to 110, which is a 10% stated return, correct? Well accourding to the formula, the answer is ln(110/100) = 9.531%. |

mtcfa |
I'll state that I may be mistaken. My note above does use the notes formula, but this question is looking for something altogether different. |

akanimo |
a) the continuously compounded rate of return in the above scenario is 9.53% (as shown by mtcfa above) b) the question is not asking for the compounded rate of return but is asking for "equivalent return" c) by definition both the stated annual return and compounded rate of return have the same S0 and S1 but state their rates under two different assumptions ... the direct rate over a period vs the rate compounded continuously over same period ... somehow the way the question is framed the answer should still be 10% ? |

faya |
Regarding the notes for this section: The HPR is the rate you're targetting. The question you will be asking is 'what continuously compounded rate results in that target HPR?'. In order to find that rate, you do: ln (1+HPR). This question is different: It is asking what the effective annual rate is, given a stated rate of 0.1. ie. what is the rate if we include interest on interest, continually compunded. Hence e^0.1 - 1. |

rufi |
YOU MIGHT BE CONFUSED COZE THERE WASNT ANY EXAMPLE LIKE THIS IN THE NOTES, BUT VERY GOOD QUESTION OVERALL |

Farina |
If needed, you can work out the CC rate using the ICONV function on the BAII+, providing you insert 365 compounding periods per year, it gives an aswer that is very close. For this it gave a rate of 10.51558% which rounds up to the correct answer of 10.52%. |

steved333 |
Yeah, gotta love ICONV. Only, it doesn't work in the other direction... |

steved333 |
Ooh, yeah it does! |

rt2007 |
in BAII+ 0.10 2nd LN -1 = .1052 |

TammTamm |
HP12C 1 enter ge^x y^x=.10 subtact one and the answer is 10.517 |

wundac |
In simpler term this question is asking the equivalent in 'return' of a 10% stated rate when continuous compounding is applied (future value). The notes were about the equivalent of return received from an investment with a discrete rate as opposed to a continuous rate (past). |

Sean12211 |
Just convert from a nominal to effective interest rate using 999999 compounding periods per year. |

Mariecfa |
The effective annual rate, based on continuous compounding for a a stated annual rate of the continuously compounded rate of return (Rcc), can be calculated from the effective annual rate. EAR = e^Rcc. Since the natural log,ln, of e^x is x, we can get the Rcc from an EAR by using the ln calculator function. ln(1 + HPR)= Rcc or ln(1 + S1/S0) = Rcc |

Jurrens |
TammTamm, you have it right (I'm using the hp12c as well), but you can just do e^(.1) - 1. Same answer, just one less step |

johntan1979 |
This is wrong. You cannot use HPR and plow that into e. This question is asking for continuous compounding, not effective annual rate (EAR). Since number of compounding is not given, we assume maximum compounding, and 365 is enough: EAR = (1 + 0.1/365)^365 -1 = 10.5156% And to get continuous compounding, it is ln (1+EAR) = ln(1.105156) = 9.9986% |

johntan1979 |
Here's an example from University of Minnesota: 4.1 A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with continuous compounding? The rate with continuous compounding is ln(1 + 0.14/4)^4 = 0.1376, i.e. 13.76% per annum. NOTE: Wharton University also gives the same method to count continuous compounding based on similar questions. |

Thediceman |
ln(CCR+1)=rt e^[ln(CCR+1)]=e^rt CCR+1=e^rt CCR=e^rt-1 |

Thediceman |
Johntan1979: For continuous compounding, let assue it compounding in min. [1+10%/(24*60*360)]^(24*60*360)-1 = 10.517105% effective rate e^10%-1=10.517092% vertually same |