PennyMac Interview Questions and Answers

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)

I listed a job that I was fired from after only a few weeks.

• Listed a job where I was fired after a few weeks

• Didn't provide a clear explanation for why I was let go

• Didn't highlight any skills or accomplishments from that job

I admire Dr. Raghunath Anant Mashelkar, an IIT Bombay alumnus, for his contributions to science and technology.

• Dr. Mashelkar is a chemical engineer and has made significant contributions to the field of polymer science.

• He has also served as the Director General of the Council of Scientific and Industrial Research (CSIR) and has been awarded numerous honors, including the Padma Shri and Padma Bhushan.

• Dr. Mashelkar has a...read more

The eurozone crisis refers to the economic and financial difficulties faced by some countries in the European Union.

• The crisis began in 2009 with the Greek debt crisis and spread to other countries in the eurozone.

• It was caused by a combination of factors including high levels of debt, low economic growth, and structural problems within the eurozone.

• The crisis led to bailouts of several countries by the European Centra...read more

The Libor Scam was a manipulation of the London Interbank Offered Rate (Libor) by banks to benefit their own trading positions.

• Libor is a benchmark interest rate used globally for financial products

• Banks were found to have manipulated the rate to benefit their own trading positions

• The scandal resulted in billions of dollars in fines for banks involved

• Several high-profile bankers were also convicted for their involvemen...read more

Derivatives are financial instruments that derive their value from an underlying asset or security.

• Derivatives can be used for hedging or speculation.

• Examples of derivatives include futures, options, and swaps.

• Derivatives can be traded on exchanges or over-the-counter.

• Derivatives can be complex and involve significant risk.

• Derivatives played a role in the 2008 financial crisis.

Failure to avoid fiscal cliff could lead to severe economic repercussions globally and in the US, with India also being affected.

• The US economy could experience a recession, with a potential decrease in GDP and increase in unemployment rates

• Global financial markets could experience volatility and uncertainty

• India could be affected due to its close economic ties with the US, with potential impacts on trade and investmen...read more

Prime Services is a suite of financial services offered by investment banks to hedge funds and other institutional clients.

• Prime brokerage

• Securities lending

• Cash management

• Risk management

• Trade execution

• Reporting and analytics

• Examples: Goldman Sachs Prime Services, J.P. Morgan Prime Services

QE stands for Quantitative Easing. It is a monetary policy used by central banks to stimulate the economy.

• QE involves the central bank buying government bonds or other securities from the market to increase the money supply.

• The increased money supply is intended to lower interest rates, encourage borrowing and spending, and boost economic activity.

• QE is typically used when interest rates are already low and traditional...read more

Find an odd occurring number among even occurring numbers.

• Use XOR operation to cancel out even occurring numbers and get the odd occurring number.

• Iterate through the array and XOR each element with the result variable.

• The final result will be the odd occurring number.

Print the spiral order of a binary tree and matrix.

• For binary tree, use level order traversal and alternate direction for each level.

• For matrix, use four pointers to traverse in spiral order.

• Example for binary tree: 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 9

• Example for matrix: 1 2 3 4 -> 8 7 6 5 -> 9 10 11 12 -> 16 15 14 13

Finding pairs in an array with a given sum.

• Iterate through the array and for each element, check if the difference between the given sum and the element exists in the array.

• Use a hash table to store the elements of the array and their indices for faster lookup.

• If there are multiple pairs with the same sum, return any one of them.

• If no pair is found, return null or an empty array.

Find total number of k element with given avg in an array in minimum time complexity.

• Use sliding window technique to traverse the array in O(n) time complexity.

• Maintain a sum variable to keep track of the sum of elements in the window.

• If the sum of elements in the window is equal to k times the given avg, increment the count.

• Move the window by subtracting the first element and adding the next element in the array.

Printing non-boundary elements of a binary tree

• Traverse the tree in any order (preorder, inorder, postorder)

• Check if the current node is not a boundary node (not the first or last node in its level)

• If it is not a boundary node, print its value

• Recursively traverse its left and right subtrees