Welcome

1. Welcome • You have been given a handset as you entered • Please don’t press any buttons yet! You may accidentally stop it working. • At the end of the session leave the handset with the attendant at each exit - Please don’t steal any – they are of no use without the rest of the system

2. When you are prompted to answer a question press the button firmly • As you vote check for the green light • If it flashes green your vote counts • If it doesn’t, try again • One vote per handset • only your most recent answer will count

3. Let’s try it out with a simple question • Remember: • Look out for thegreen light on the handset which flashes top indicate that your vote has been received • No need to hurry….

4. How did you travel to university today? • Tube/train • Bus • Bicycle • Walking • Other This slide shows…?

5. Excel for advanced calculations John Cubbin

6. Outline Week 1 • Excel from basics to advanced functions Week 2 • Excel add-ins and introductory programming ideas, recording macros Week 3 • Amending recorded macros using VBA programming language

7. Applications Week 1 • Portfolio mean and variance Week 2 • Simple Monte Carlo analysis Week 3 • Revision

8. Reading • Mary Jackson, Mike Staunton Advanced modelling in finance using Excel and VBA Wiley 2001. • Chapters 2-3 possibly 4 for more advanced students

9. Have you used Excel before? • No, not really • For elementary operations only • For moderately complex calculations • Have recorded macros • Can program in VBA

10. Have you worked in the finance or economics area before? • Yes • No • Not sure

11. What can Excel do in Finance? Examples of problem 1. Demonstrating key concepts 2. Portfolio selection 3. Option pricing 4. Value at risk 5. Non-lognormal returns Methodologies 1. Simulation of markets:Monte Carlo and bootstrapping 2. Numerical solution of problems with no analytic solution

12. Advantages and disadvantages of Excel Advantages • Wide range of powerful techniques • Input and output need little programming • Example 1 • Disadvantages • Not a compiled language • Slower than specialised mathematical programming languages

13. Good practice in spreadsheet work Other people (and yourself later) may need to work out what on earth is going on! It is not easy to know. Example 2 • Transparency • Make it clear what is going on • Group obvious things together • Keep background stuff out of the way • Documentation • Where it is not self evident, add labels, comments etc.

14. Good practice (2) • Auditing –necessary to ensure accuracy • Make use of check sums and conditional formatting to trap errors • Use the formula auditing tool box to make sure your intentions have been fulfilled • Do a series of calculations where you know the correct answer to make sure you are returning sensible results • In important applications, get another person to audit and comment on your work

15. How am I getting through? Am I going… • Too slow • About right • Too fast?

16. How much is new? • All this is new to me • Most is new to me • Some things are new to me • I knew almost all this before

17. To test your understanding, the Rand() function in Excel: • Creates a normally distributed variable • Creates a number entirely at random • Replicates the throw of a die • Creates a uniform distribution in the range {0,1}

18. Section 2: More advanced functions

19. More advanced functions • Arrays • Frequency • Lookup • Regression approaches • Random number generation

20. Arrays 1xN, NxN, Nx1, NxM Each array can be given a name as follows: Select a range From the menu select Insert…, Name, Define If there is a label at the top or side of the array this will be the default name

21. Frequency Counts the cells with a given frequency Format is Frequency( data array, bins array) The key to using formulae covering a whole array is to press CTRL +Shift+ Enter instead of Enter when you have entered the formula. See Example 3

22. Lookup See Example 4

23. Regression Three ways (at least) to do regression: 1. Program all the formulae yourself Dynamic 2. Use Statistical functions Intercept, slope, RSQ, etc Dynamic 3. Use Linest Array function Dynamic 4. Use Data Analysis Add-In, Regression Analysis Static

24. Random Number Functions Much literature on random numbers - In real life applications, make sure you get a good one with long cycle time - For teaching purposes, Excel functions work fine - You have already come across Rand(), which gives an outcome in the range {0,1}. This is dynamic - This can be used to create other random distributions

25. Turning Rand() into a normal distribution 1 Cumulative probability F The inverse of F does the opposite F converts a Standard Normal distributed variable into a variable in the range {0,1} We can use this fact to convert a uniform random variable into a normally distributed variable Z 0 The Excel command is NormSInv(Prob) This is a clever trick which can be used with other probability functions whose cumulative function has an inverse

26. Static random numbers In Tools…Data analysis… You can generate number of different distributions. However these are generated just once and not recalculated. Rand() is recalculated every time. To stop this happening you can do Copy... Paste Special…Values

27. Random number generation… • Can be done different ways in Excel • Needs care in selection for proper research • Is helped by the use of an inverse function • All of the above

28. To create an array variable press… • CTRL+ Shift + Del • Alt+ Shift+ Enter • CTRL +Shift +Enter

29. Homework First program the following in Excel: The expected returns on a portfolio of two assets X1 and X2 with returns R1 andR2 is RE = w1R1 +w2R2 ; In a specific case R1 =10% R2=3% SD1 = 0.15 SD2 = 0.02 Correlation coefficient r (X1X2) = 0.1 Work out the portfolio that would be required to earn an expected return of 7.2%. What is the standard deviation of this portfolio’s returns? Recall that the variance of a weighted average is w12Var(X1) + w22Var(X2) -w1w2Cov(X1X2) and r = covariance /(sqrt of product of variances)

30. This questions looks… • Very difficult • Challenging but do-able • Do-able with some effort • Quite easy • Wrongly conceived

31. Homework continued Next be prepared to discuss the following questions: • How can you be sure this is the correct answer? • How would you generalise this spreadsheet for multiple assets? You may work in groups of 2 or 3

32. Please remember to return Handsets