FE 459
Spring 2025

Exam Information

Exam details

Material covered

The exam will be comprehensive on the content ofFE459.

The exam will focus on the material that we have discussed in class during the first half of the course. The exam will cover both finance and programming topics, in approximately equal proportion.

Approximately 25% of the exam will focus on material from weeks 1-7 of the course.

You should review all of the material from the practice problems for the midterm exam.

The remainder of the exam (approximately 75%) will be focused on material from the last 6 weeks of the course, including:

Conceptual finance topics include:

Programming topics include:

Preparing for the exam

Sample Conceptual Questions

Note: this is a sampling only, and NOT a study guide.

  1. Explain how the binomial option pricing model simulates the future stock price. Make and argument for why this is a reasonable strategy.

  2. With regards to the Black-Scholes option pricing formula:

    Identify and briefly explain the parameters (inputs) to this formula, and the effect of each on the resulting option price. (i.e., how does the option price change with an increase in each of the inputs?)

  3. With regards to the Black-Scholes option pricing formula:

    Most of the parameters are observable, expect for the volatility of returns. Explain the concept of implied volatility, and how to calculate it.

  4. In one assignment, we used Monte Carlo simulation to value several kinds of stock options.

    a. Explain the fundamental ideas/methods of Monte Carlo methods to find the price path of a stock.

    b. How can we use the simulated stock price path to compute the value of a
    lookback call option, where the payoff is the maximum stock price minus the strike price?

  5. In one assignment, we created mean-variance efficient portfolios, and created the efficient frontier for a set of assets.

    a. Explain: what is a mean-variance efficient portfolio? How do we represent such a portfolio?

    b. Explain the process/algorithm by which you created the efficient frontier. (no formulas are required, but you must explain the process)

  6. With regards to the value at risk (VaR):

    a. Explain: what does VaR measure, and why is it useful?

    b. One method that we discussed to compute VaR involved using a statistical model-based approach to quantifying the value at risk. Briefly explain how the model-based approach works, and identify the main shortcomings of this approach. (no formulas are required, but you must explain the process)

    c. One method that we used to compute VaR involved historical data. Explain how this worked, and why is this an reasonable approach. (no formulas are required, but you must explain the process)

  7. Our last assignment used databases and SQL.

    a. Explain, giving an example, the purpose of the SQL JOIN clause, and how it is used.

    b. Explain, giving an example, the purpose of the SQL GROUP BY clause, and how it is used.

Sample Programming Problems

Review/solve all practice problems from the midterm exam

Note: this is a sampling only, and NOT a study guide.

  1. Assume the class definition for the class Vector has already been provided. Write a dot_product method that will compute the dot product of two Vectors. The method should return a scalar result, or else print out an error message and return None. You may not use the numpy library. Here is a usage example:

    >>> v1 = Vector([3, 4, 5])
>>> v2 = Vector([1, 2])
>>> v3 = Vector([3, 4])
>>> v2.dot_product(v3) # 1*3 + 2*4 = 11
11
>>> v1.dot_product(v2)
Error: lengths do not match for dot product. 
>>> v1.dot_product(42) # integer parameter
Unspecified error.

  2. Assume a class called Price, which contains a data attribute value.

    a. Create a subclass called StockPrice, which inherits from Price, and defines a new data attribute symbol.

    b. Write a constructor for this class, and be sure to initialize the superclass with the data attribute value.

    c. Define a __repr__ method to return a string representation of this object.

    d. Write an __eq__ method that makes it possible to compare a Price with a StockPrice.

  3. Given the following statement: 

    a = np.array([[1,2,3],[4,5,6]])
b = np.array([[1,2],[3,4],[5,6]])
c = np.array([[1,2,3,4],[5,6,7,8]])

    Write a one-line expression to produce each of the following:

    a. The element of a with value of 5 b. A slice of the row of a containing: [4, 5, 6] c. A slice of the sub-array of c containing the values [[2, 3], [6, 7]] d. The column vector containing the sum of elements from the first two columns of a e. The dot-product of b and c

  4. Assuming a pandas DataFrame df has been created. Use the correct syntax to retrieve:

    a. a slice containing the 2nd row

    b. a slice containing the 2nd column

    c. a slice containing the column identified by the label ‘price’

    d. the value of the column ‘price’ in the 2nd row

    e. a slice containing the last row

    f. insert a new column of 0s

    g. create a plot of the column ‘price’

    h. Use the values in the column ‘price’ to create a pandas series of returns.

  5. Assuming a pandas DataFrame df of daily stock prices for two stocks A and B. Write a function to calculate the daily returns of an equal-weighted portfolio of these two stocks.

    Your function should return a pd.Series of daily portfolio returns.

  6. Recall that drawdown is a measure of the maximum loss on an asset since its previous maximum price. Given a pd.Series of stock prices, write the function compute_drawdown(prices) that returns a pd.DataFrame object containing the columns ['price', 'prev_max', 'dd_dollars', and 'dd_pct'].

    Here is an example of calling this function:

    >>> dd = compute_drawdown(prices)
>>> dd
   price  prev_max  dd_dollars    dd_pct
0     16        16           0  0.000000
1     14        16           2  0.142857
2     13        16           3  0.230769
3     17        17           0  0.000000
4     14        17           3  0.214286