Pershing Interview Questions and Answers

A bond is a debt security that represents a loan made by an investor to a borrower.

• Bonds are issued by corporations, municipalities, and governments to raise capital.

• They have a fixed interest rate and a maturity date when the principal is repaid.

• Bonds are generally considered less risky than stocks but offer lower potential returns.

• Investors can buy and sell bonds on the secondary market.

• Examples of bonds include U.S....read more

Fund Accounting is a specialized accounting system used by non-profit organizations and government agencies to track and manage funds.

• It involves tracking and reporting on the financial activity of specific funds or grants.

• It ensures that funds are used for their intended purposes and that financial reports are accurate and transparent.

• Examples include tracking donations to a non-profit organization or managing governm...read more

Prototyping in JavaScript allows for quick and easy creation of new objects and functions.

• Prototyping allows for inheritance and sharing of properties and methods.

• New objects can be created using the 'new' keyword and the prototype of an existing object.

• Functions can also be prototyped to add new methods or properties.

• Example: function Person(name) { this.name = name; } Person.prototype.greet = function() { console.log...read more

Amortization is the process of spreading out a loan into smaller, regular payments over a period of time.

• It is used to pay off a debt over time with regular payments

• Each payment includes both principal and interest

• The amount of interest decreases over time as the principal is paid off

• Examples include mortgages, car loans, and student loans

WASO is Wake After Sleep Onset, TSO is Total Sleep Time, and EPS is Earnings Per Share.

• WASO is the amount of time spent awake after initially falling asleep.

• TSO is the total amount of time spent sleeping, including both REM and non-REM sleep.

• EPS is a financial metric that represents the portion of a company's profit allocated to each outstanding share of common stock.

• WASO and TSO are commonly used in sleep studies, whi

The financial statements (BS, IS, CF) have common elements such as assets, liabilities, equity, revenue, expenses, and cash flows.

• Assets: resources owned by the company

• Liabilities: obligations owed by the company

• Equity: residual interest in the assets of the company

• Revenue: income generated by the company

• Expenses: costs incurred by the company

• Cash flows: inflows and outflows of cash

A stock split increases the number of shares outstanding and decreases the price per share, but does not affect the market capitalisation.

• Stock split does not affect the total value of the company

• Market capitalisation remains the same after a stock split

• Stock split increases the number of shares outstanding and decreases the price per share

• For example, if a company has 1 million shares outstanding and the stock splits ...read more

Cash flow statements have three main components: operating activities, investing activities, and financing activities.

• Operating activities: cash inflows and outflows from the company's core business operations.

• Investing activities: cash inflows and outflows from buying or selling long-term assets.

• Financing activities: cash inflows and outflows from borrowing or repaying debt, issuing or buying back stock, and paying di...read more

EPS is calculated by dividing the company's net income by the number of outstanding shares.

• EPS = Net Income / Outstanding Shares

• Net Income is the company's total earnings after expenses and taxes

• Outstanding Shares are the total number of shares issued by the company

• EPS is an important metric for investors to evaluate a company's profitability

• Higher EPS indicates better profitability and potential for higher dividends

Morgan Stanley is a top-tier investment bank with a strong reputation for innovation and excellence.

• Morgan Stanley has a long history of success in the financial industry

• The company is known for its innovative approach to investment banking

• Morgan Stanley has a strong reputation for excellence in research and analysis

• The firm offers a wide range of services to clients, including wealth management and investment banking

• M...read more

Tower and Morgan Stanley are both financial services companies.

• Tower is a global investment management firm with over $1 trillion in assets under management.

• Morgan Stanley is a multinational investment bank and financial services company.

• Both companies offer a range of financial services including wealth management, investment banking, and asset management.

• Tower is known for its focus on sustainable investing, while Mo...read more

The job profile offered is for an analyst position. A PhD is not required for this role.

• The job involves analyzing data and providing insights to clients

• A PhD is not necessary as the role focuses more on practical application of analytical skills

• The job may require a bachelor's or master's degree in a related field

• Examples of job responsibilities may include data collection, statistical analysis, and report writing

Innovations to minimize cost of pen

• Use recycled materials for pen body and ink

• Simplify design to reduce production costs

• Implement refillable ink cartridges to reduce waste and cost

• Partner with companies for bulk purchasing of materials

• Automate production process to reduce labor costs

Prove N>=N^.5+N^(1/3)+N^(1/4) for N>=a

• Use AM-GM inequality

• Substitute N with a and prove the inequality holds

• Use calculus to find the minimum value of the expression

Finding the probability distribution for the minimum of two random variables with given distributions.

• Use the formula P(min(x,y)>z) = P(x>z)P(y>z)

• Integrate over the range of z to get the distribution of min(x,y)

• Final distribution is 2ke^(-kx)ue^(-ux)exp(-uz)

Given prob. p of dying out and prob. (1-p) of spawning into 2, find prob. of dying out starting from 1 organism.

• Use probability tree to visualize outcomes

• Probability of dying out starting from 1 is p + (1-p) * (probability of dying out starting from 2)^2

• Solve recursively to get final answer

Probability of a rectangle being inside a unit circle with p chosen uniformly on the circle and q inside the circle.

• The probability can be found by calculating the ratio of the area of the rectangle to the area of the circle.

• The area of the circle is pi and the area of the rectangle can be found using the distance between p and q.

• The probability is 1/4.

• Example: If the distance between p and q is 0.5, then the area of t...read more

Find local minima of an array in o(log n) in functional programming.

• Use binary search to find the local minima.

• Check if the mid element is a local minima, if not, move towards the lower side.

• If the mid element is greater than its left element, move towards the left side, else move towards the right side.

• Repeat until a local minima is found.

• Example: [5, 3, 2, 4, 6, 8, 9] -> local minima is 2.

Code to sort a list without pipes

• Use a sorting algorithm like bubble sort, insertion sort, or selection sort

• Implement the algorithm in the programming language of your choice

• Test the code with different input sizes and types

To find an even length palindrome in a string in O(n), we can use the two-pointer approach.

• Initialize two pointers at the center of the string.

• Expand the pointers outwards while checking if the characters at both pointers are equal.

• If they are not equal, return the previous substring as the even length palindrome.

• If the pointers reach the end of the string, return the entire string as the even length palindrome.

Possible values of determinant of matrix A given Avi=Vj for n linear vectors

• The possible values of |A| are non-zero as the given vectors are linearly independent

• The value of |A| can be calculated using the formula |A| = (-1)^n * det(A)

• If the given vectors are orthogonal, then |A| is the product of the magnitudes of the vectors

A and B play a game with unfair coin. A wins if # of heads > #tails +1 at any point. Find prob. of A winning.

• The game is played with an unfair coin with P[Heads]=p

• A wins if # of heads > #tails +1 at any point

• Find the probability of A winning

Find two elements in a sorted array that add up to a given sum in linear time.

• Use two pointers, one at the beginning and one at the end of the array.

• If the sum of the two pointers is greater than the target, move the right pointer to the left.

• If the sum of the two pointers is less than the target, move the left pointer to the right.

• Repeat until the sum is found or the pointers meet.

• Example: Given [1, 2, 3, 4, 5] and ta

The probability of element at 20th position landing up at 31st position after the first iteration.

• The probability depends on the size of the dataset and the algorithm used for iteration.

• If the algorithm involves swapping adjacent elements, the probability is higher.

• If the dataset is sorted in a way that the element at 20th position is adjacent to the element at 31st position, the probability is 1.

• The probability can be...read more

Expected number of collisions between randomly moving ants on a rod after 30 seconds.

• Calculate the probability of two ants colliding at any given time.

• Use the formula for expected value to find the expected number of collisions.

• Assume that the ants are point masses and collisions are perfectly elastic.

• Consider the possibility of multiple ants colliding at the same time.

• Simulation can also be used to estimate the expect

Counting permutations where numbers between u and i+1 are less than i for all i in the permutation.

• The first number in the permutation must be 1.

• For each i in the permutation, all numbers between u and i+1 must be less than i.

• Use dynamic programming to count the number of valid permutations.

• The answer is (n-1)th Catalan number.

• Example: for n=4, the answer is 5.

Finding f(n) for a normal standard distribution with a given constant k.

• Calculate the product of probability density function and cumulative distribution function.

• Integrate the product of f(x) and F(kx) from -inf to +inf.

• The value of k is a constant greater than 0.

Number of inversions in an array in O(nlogn) time.

• Use merge sort algorithm to count inversions

• Divide the array into two halves and recursively count inversions

• Merge the two halves and count split inversions

• Time complexity is O(nlogn)