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This slide shows…?

Excel for advanced calculations

John Cubbin

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

Week 1

- Portfolio mean and variance
Week 2

- Simple Monte Carlo analysis
Week 3

- Revision

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

- No, not really
- For elementary operations only
- For moderately complex calculations
- Have recorded macros
- Can program in VBA

- Yes
- No
- Not sure

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

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

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.

- 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

- Too slow
- About right
- Too fast?

- All this is new to me
- Most is new to me
- Some things are new to me
- I knew almost all this before

- 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}

Section 2: More advanced functions

- Arrays
- Frequency
- Lookup
- Regression approaches
- Random number generation

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

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

See Example 4

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

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

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

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

- 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

- CTRL+ Shift + Del
- Alt+ Shift+ Enter
- CTRL +Shift +Enter

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)

- Very difficult
- Challenging but do-able
- Do-able with some effort
- Quite easy
- Wrongly conceived

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

Please remember to return Handsets