Notes, abstracts, papers, exams and problems of Mathematics

Part I: Complete the Following Table

Part II: Complete the Following Sentences

1. She is from the United States. She is American.
2. She is from Nigeria. She is Nigerian.
3. She is from Germany. She is German.
4. They are from Egypt. They are Egyptian.
5. We are from Canada. We are Canadian.

Part III: Select the Correct Sentence

1. Select the correct sentence.
   • a) She lives with Carlos, and she works on Saturdays.
2. Select the correct sentence.
   • c) They are running in the park.
3. Select the correct sentence.
   • b) She is 20 years old.
4. Select the correct sentence.
   • a) We always

Bond Characteristics

• Coupon: The interest payment made by the bond issuer, usually expressed as an annual percentage of the bond's face value.
• Par (Face Value): The amount the bondholder receives when the bond matures, typically $1,000.
• Term to Maturity: The time remaining until the bond's maturity date when the issuer must repay the bond's par value.
• Denomination: The face value of the bond, usually in increments of $1,000.
• Quotation: Bonds are quoted as a percentage of their face value (e.g., a bond quoted at 95 is selling for 95% of $1,000, or $950).

Bond Prices, Yield to Maturity (YTM), Current Yield, and Rate of Return (HPR)

• Bond Prices: The market price of a bond depends on interest rates. Prices and interest rates have an inverse relationship.

Discrete Random Variables

Discrete random variables are variables that can take on a finite number of distinct values. In simpler terms, a discrete random variable is a set of possible outcomes that is countable.

Continuous Random Variables

Continuous random variables are random variables that take an infinitely uncountable number of potential values, typically measurable amounts.

Example

1. List the sample space in the given experiment. How many outcomes are possible?

The sample space is: S = {NNN, NND, NDN, NDD, DNN, DND, DDN, DDD}

2. Count the number of defective keyboards in each outcome in the sample space and assign this number to the outcome. For instance, if you list NND, then the number of defective keyboards is 1.

The possible values of X are 0,... Continue reading "Introduction to Statistics: Discrete and Continuous Random Variables, Probability Distributions, and Sampling Techniques" »

Inventory Fundamentals

One use of inventory is to provide a hedge against inflation. ABC analysis divides an organization's on-hand inventory into three classes based upon annual dollar volume. Cycle counting is a process by which inventory records are verified. The difference(s) between the basic EOQ model and the production order quantity model is that the production order quantity model does not require the assumption of instantaneous delivery. Extra units that are held in inventory to reduce stockouts are called safety stock. Inventory record accuracy would be decreased by increasing stockroom accessibility. The two most important inventory-based questions answered by the typical inventory model are when to place an order and how many of

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Write an interpretation of r^2 using the template in the Activity 2.1 Readings. We will do this one as a class.

Template: The proportion of the variation in the Y variable that is explained by the SLR model with the X variable is r^2.

For slope : Template: As x var increases by 1 unit, we predict y var  will increase/dec  by ____  y var units.

For y-intercept: When x var = 0 units, we predict that the y var  will be ____ units..

For SLR: Error = epsilon = y - yhat = y - (betahat0 + betahat1x)

SSE = residual1^2 + res. 2^2 +…+ res.  n^2

Standard error of regression = Root MSE (in SAS language)

The text lists six conditions for simple linear... Continue reading "Understanding Simple Linear Regression: R-squared, Slope, and Conditions" »

Key Principles of Financial Budgeting

Entity Principle

Consider the company as a functional entity.

Leadership Principle

The Financial Planning Manager develops and coordinates the budget.

Authority Principle

The Finance Manager supervises and presents the budget to the Board of Directors (Partners).

Participation Principle

Involve all key participants in the budget's preparation.

Commitment Principle

All managers undertake to follow the budget, notifying any deviation in a timely manner.

Goal Principle

The budget is based on the strategic planning objectives.

Accounting Principle

A budget system should mirror the current accounting system.

Measurement Principle

All estimates must be in currency units.

Predictability Principle

The predictions generated must... Continue reading "Financial Budgeting: Principles and Model Development" »

Consider an European call option with strike equal to 10, T = 1, r = 0.05 and σ = 0.2. Using the following time-series:

1. For every time moment t = 0, 1/360, 2/360:

• Calculate the Black-Scholes price.
• Calculate the corresponding delta.
• Calculate the price of the corresponding replicating portfolio and its composition, if we consider a dynamic hedging.

2. Calculate a static hedging. What is the final value of the portfolio? Compare with the dynamic hedging results.

Solution

• At time 0, time to maturity is 1, and then
  • The Black-Scholes price is given by S0N(d1)−Ke−rT N(d2) = 10N(0.35)−10e−0.05N(0.15) = 1.0450
  • The Delta is given by N(d1) = N(0.35) = 0.6368
  • At time t = 0, the value of the replicating portfolio coincides with the Black-Scholes price

Mathematical Aptitude - Average

Question 1

The average age of 30 students is 9 years. If the age of their teacher is included, it becomes 10 years. The age of the teacher (in years) is

_______

(A) 31

(B) 35

(C) 40

(D) 43

Question 2

The average weight of 10 men is decreased by 3 kg when one of them whose weight is 80 kg is replaced by a new person. The weight of the new person is

_______

(A) 50

(B) 60

(C) 70

(D) 73

Question 3

The average of 17 numbers is 45. The average of the first 9 of these numbers is 51 and the last 9 of these numbers is 36. What is the ninth number?

(A) 14

(B) 16

(C) 18

(D) 20

Question 4

The average weight of 9 mangoes increases by 20 gm if one of them weighing 120 gm is replaced by another. The weight of the new mango is

________

(A) 180 gm

(B)... Continue reading "Mathematical Aptitude Test: Average Practice Questions" »

Management of Interest Rate Risk

Major Risks in Bond Market

A) Interest Rate Risk (change in market prices of bonds due to varying interest rates)

• Increase in rates, decrease in market prices, increase in reinvestment rate risk (coupons reinvested at lower return)

B) Reinvestment Rate Risk (uncertainty of rate at which interim cash flows can be reinvested)

• High coupon rate, high reinvestment rate risk
• Greater for longer holding periods (high interim cash flows)

C) Default Risk (credit risk) (issuer unable/unwilling to pay interest and principal of bond)

• High credit rating, lower yield
• Short-term T-bills (almost risk-free, no default risk, and low return and reinvestment risk because of short duration)

D) Call Risk (risk bond issuer will redeem bond before... Continue reading "Interest Rate Risk Management: A Comprehensive Guide for Investors" »