1. Practical 4: Dollar Cost Averaging, Compounding and Statistical Excel Functions Gopalan Vivek vivek@bic.nus.edu.sg

2. Objectives Statistical functions – MAX, MIN, AVERAGE, MODE,MEDIAN Compounding Dollar Cost Averaging Complete questions in Practical 4 given below http://chaos.nus.edu.sg/Teaching/SCC2301/Practicals/practical1.p pt http://chaos.nus.edu.sg/Teaching/SCC2301/Practicals/practical1.p pt

4. Common Statistical Functions MAX – returns maximum of a range of cell values MIN – returns minimum of a range of cell values. AVERAGE – returns average or mean of cell values.

5. Statistical Functions MEDIAN – Returns middle value of an ordered array. – Unaffected by the outliers, thus most appropriate measure of central tendency when outliers are present in the data MODE – Returns the most frequently occurring, or repetitive, value in an array or range of data. – Not affected by outliers Check the help for other Statistical functions in Excel

6. Statistical Functions - Excel Hints The arguments should be numbers, names, arrays, or references that contain numbers. If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included. If the data set contains no duplicate data points, MODE returns the #N/A error value. If there is an even number of numbers in the set, then MEDIAN calculates the average of the two numbers in the middle. - Obtained from Excel help

7. Statistical Functions - ? 1. What value does AVERAGEA function in Excel returns ? 2. What Excel function is used to calculate the third and fourth largest numbers of the following set 1,4,6,7,25, 28, 8,12, 20, 22, 24 ? Solve the question no. 1 in the practical 4 http://chaos.nus.edu.sg/Teaching/SCC2301/Practicals/practical_4.html

8. Power of Compounding http://mutualfunds.about.com/library/we ekly/aa112100a.htm http://mutualfunds.about.com/library/we ekly/aa112100a.htm http://www.rrsp.org/compounding.htm http://www.moneycontrol.com/planning_ desk/powerofc.php http://www.moneycontrol.com/planning_ desk/powerofc.php "Compounding interest is the greatest mathematical discovery of all time". Albert Einstein

9. Compounding calculations in Excel FV function FV function is used for the calculation of Compounding problems in Excel

10. Formula - Obtained from Excel help

11. Arguments FV (rate, nper, pmt, pv, type ) –Rate is the interest rate per period. –Nper is the total number of payment periods in an annuity. –Pmt is the payment made each period; it cannot change over the life of the annuity. Typically, pmt contains principal and interest but no other fees or taxes. If pmt is omitted, you must include the pv argument. –Pv is the present value, or the lump-sum amount that a series of future payments is worth right now. If pv is omitted, it is assumed to be 0 (zero), and you must include the pmt argument. –Type is the number 0 or 1 and indicates when payments are due. If type is omitted, it is assumed to be 0. - Obtained from Excel help

12. FV function Arguments criteria Make sure that you are consistent about the units you use for specifying rate and nper. – If you make monthly payments on a four-year loan at 12 percent annual interest, use 12%/12 for rate and 4*12 for nper. If you make annual payments on the same loan, use 12% for rate and 4 for nper. cash you pay out, such as deposits to savings, is represented by negative numbers cash you receive, such as dividend checks, is represented by positive numbers. - Obtained from Excel help Solve the question no. 2 in the practical 4 http://chaos.nus.edu.sg/Teaching/SCC2301/Practicals/practical_4.html

13. Dollar Cost Averaging (DCA) - definition An investment strategy designed to reduce volatility in which securities, typically mutual funds, are purchased in fixed dollar amounts at regular intervals, regardless of what direction the market is moving. Thus, as prices of securities rise, fewer units are bought, and as prices fall, more units are bought. http://www.investorwords.com/ As mentioned in your practical web page go to your favorite search engine and find out more about dollar cost averaging (DCA)

14. DCA – Simple e.g. A person has invested 100 dollar/month in stock market by dollar cost averaging. The share price values of the stocks he bought for 6 months are given as What is the value of his total investment after 6 months ?

15. DCA - Answer

16. Dollar Cost Averaging http://www.statelinebusiness.com/501/mony5.htm http://www.westcore.com/InvestorEd/reg-invest.asp http://www.datalife.com/mall/pages/examples/EXMP_ DCA.HTM http://www.datalife.com/mall/pages/examples/EXMP_ DCA.HTM http://www.phn.com/planni/planni_featur_dollar.asp http://www.cifunds.com/web/straighttalk/straight.jsp?l ang=ENG&no=5 http://www.cifunds.com/web/straighttalk/straight.jsp?l ang=ENG&no=5 http://www.ameritrade.com/educationv2/fhtml/learnin g/dolcstave.fhtml http://www.ameritrade.com/educationv2/fhtml/learnin g/dolcstave.fhtml

17. U. S. Stock Markets – e.g. New York Stock Exchange (NYSE) American Stock Exchange (AMEX) National Association of Securities Dealers (NASDAQ) http://faculty.fuqua.duke.edu/~mroberts/Teaching/LectureSlides/Class2_Stocks_Slides_Handout.pdf

18. International Stock Markets – e.g. http://faculty.fuqua.duke.edu/~mroberts/Teaching/LectureSlides/Class2_Stocks_Slides_Handout.pdf

19. Dow Jones Industrial Average the average of 30 bull chip stocks hand picked by the Wall Street Journal editors – DOW 30 The dow is an indication of the well being of the overall market. http://www.dowjones.com/

20. Solve the ‘Effect of compounding’ question (question no. 4) in the practical 4 and submit your answers http://chaos.nus.edu.sg/Teaching/SCC2301/Practicals/practical_4.html