Notes, summaries, assignments, exams, and problems for Mathematics

Financial Market Scenarios: Fixed Income and Derivatives

Sildavia: Term Structure and Yield Curve Construction

In Sildavia's financial market, we assume the existence of a series of zero-coupon bonds and conventional bonds. Each bond type presents specific traits:

• Zero-Coupon Bonds: Defined by spot rates and coupon interest rates.
• Conventional Bonds: Defined by specific characteristics (data assumed to be provided in an accompanying table).

Based on the provided data, the objective is to construct the TSIR (Term Structure of Interest Rates) and the Yield Curve for both kinds of bonds.

Moravia: Calculating Forward Rates

Considering the TSIR shown in Table 1, calculate the corresponding forward rates (r_t).

Furthermore, if the market involves an inverted

This document outlines the steps to calculate production costs, including equivalent units and costs for work-in-progress (WIP) and finished goods.

1. What does boot mean?
2. How to determine the basis of taxable and non-taxable stock dividends?
3. How to determine if a gain is long-term or short-term?
4. How does capital gain/loss netting work?
5. What is the tax rate of regular long-term capital gain? [0%, 15%, 20%]
6. Individual taxpayers can deduct net capital loss (short-term or long-term) up to $3,000 per year.
7. The maximum tax rate for collectibles is 28%; the maximum tax rate for unrecaptured Section 1250 gain is 25%.
8. How to determine amount realized? How to determine amount realized when there is debt assumption?
9. What is unrecaptured Section 1250 gain? How to calculate it?
10. What is the basis of gifts? How to determine the holding period of a gift?
11. How to determine the adjusted basis?
12. How to determine realized

Monthly Financial Data

1. Present Value of an Investment

15 Years Case

Present Value of the Investment = $4,900 [ (1/0.08) − (1/0.08(1 + 0.08)^15)] = $41,941.45

2. Effective Annual Rate (EAR)

EAR = (1 + (APR/m))^m − 1 If m becomes infinite, EAR = e^APR − 1

7% APR and quarterly compounding: EAR = (1 + (0.07/4))^4 − 1 = 7.19%

16% APR and monthly compounding: EAR = (1 + (0.16/12))^12 − 1 = 17.23%

11% APR and daily compounding: EAR = (1 + (0.11/365))^365 − 1 = 11.63%

3. Value of a Perpetual Stream of Payments

Present Value of the Perpetuity = (Payment/Interest Rate) Payment = $2,500, Interest Rate = 0.061

PV of the perpetuity at date t=14 is $2,500/0.061 = $40,983.61. Discounting it back to date t=7, we should have PV7 = $40,983.61/(1+0.061)^7 = $27,077.12.

4. Bond

Operationalizing Concepts

Operationalizing involves transforming abstract concepts into measurable and tangible factors. This is achieved by examining the behavioral dimensions, facets, or properties associated with the concept. For instance:

• Achievement Motivation: Measured by observing behaviors like the inability to relax or constantly thinking about work, even at home.

Structured Observation

Structured observation is the systematic recording of predetermined behavioral patterns of individuals, objects, and events. Examples include:

• Personal Observation: Mystery shopping, pantry audits
  • Advantages: Clarifies questionnaire doubts, captures non-verbal cues.
  • Disadvantages: High cost, time-consuming, geographical limitations, potential for response

CS 206 Spring 2016, Rutgers University

Prof. David Cash

March 27, 2016

General Advice for Exam Preparation

This preparation document is meant to help you prepare for Midterm 2. It does not contain any new problems or topics. Instead, it places everything we've covered in one place, and isolates some specific skills that will be tested in the exam.

Learning math (or, more specifically, learning problem-solving skills in order to do well on an exam) is a highly personal activity. But I can describe how I learn math, in the hope that my opinion will be useful.

To learn basic topics, like how to compute simple conditional probabilities, one can actively work through solved examples, especially the ones from class. While this is an important first step,... Continue reading "CS 206 Midterm 2 Preparation: Story Proofs and Probability Skills" »

) What is the difference between PEST, PESTEL, STEEPLE, and SLEPT Analysis?

16.) What are a corporation's dynamic capabilities and why is it important to be aware of them as part of the strategic management process?

17.) Different internationalization strategies are normally compared based on two main dimensions. What are these two dimensions and why were they originally chosen by companies to compare their internationalization strategies?

18.) How can a company create competitive advantage in its most basic form?

19.) What are sources of competitive advantage?

20.) What is the next step after you have conducted a PEST Analysis? How do you use such an Analysis?

21.) In class we discussed four basic levels of internationalization. Name and compare... Continue reading "International Business and Global Competitiveness: Key Concepts and Strategies" »

Essential Math Formulas and Concepts

Volume of Shapes

(a) Cube:

• Formula: V = s³ (where s is the length of a side)
• Example: A cube with side length 4 cm

V = 4³ = 64 cm³

(b) Cylinder:

• Formula: V = πr²h (where r is the radius and h is the height)
• Example: A cylinder with radius 2 cm and height 6 cm

V = π(2²)(6) = 24π cm³ (approximate value)

Surface Area of Shapes

(a) Cube:

• Formula: SA = 6s² (where s is the length of a side)
• Example: A cube with side length 3 cm

SA = 6(3²) = 54 cm²

(b) Cone:

• Formula: SA = πr(r + √(r² + h²)) (where r is the radius and h is the height)
• Example: A cone with radius 5 cm and height 8 cm

SA = π(5)(5 + √(5² + 8²)) = 129.74 cm² (approximate value)

Stem and Leaf Plot

(a) Mean:

• Example: Data: 5, 7, 8, 9, 10, 12, 15

Mean = (5 + 7 + 8... Continue reading "Essential Math Formulas and Concepts: A Quick Reference" »