Consider a multi-aspect key rate model with key rates being YTM on 2, five, 10, and 30-yr par ponds. Assume also that currently YTM on 2, 5, 10, and 30-12 months bonds are four%, five%, 6%, and seven% respectively. Assume all bonds have a $100 face fee. Keep at the least 6 decimal digits.

A) (2 factors) Find KR012 for two-yr par bond; KR015 for 5-year par bond; KR0110 for 10-12 months par bond; and KR0130 for 30-12 months par bond

b) (1 point) Find all key costs (KR012, KR015, KR0110, and KR0130) for a fifteen-year par bond if YTM for this bond is 6.25%

c) (1 factor) Find all key charges (KR012, KR015, KR0110, and KR0130) for a 20-12 months par bond if YTM for this bond is 6.Five%

d) (1 point) Find all key quotes (KR012, KR015, KR0110, and KR0130) for an 8-12 months par bond if YTM for this bond is five.6%

e) (1 point) Find all key rates (KR012, KR015, KR0110, and KR0130) for a 6-year par bond if YTM for this bond is 5.2%

f) (6 factors) You would like to hedge your portfolio that includes one thousand 6-12 months par bonds using 2, eight, 15, and 20 bonds. How might you do it? Please, specify the quantity of each bonds (quantity of bonds for each form of bonds) you should purchase or sell (observe you can come to be the usage of just a few of those bonds). Use the KR01 quotes you determined earlier and make sure to write down the machine of equations you want to remedy earlier than looking to solve it. [9:51 AM, 11/14/2021] .: Choose 4 actual securities and acquire 5 years of monthly buying and selling records for them. In facts science it is not unusual to educate a model on a first set of facts, then check it on the second set. Using best the first three years of information, chart the danger-go back profile of each protection as well as a variety of fixed-weight portfolios comprised of the four ingredients. Assume a threat-loose go back of 1% per year. Find the tangent portfolio (what are the weights?) and encompass the capital market line at the danger-go back chart. Compute the beta for each protection with admire to the Tangent Portfolio in approaches: because the slope of the regression among security returns and Tangent portfolio returns and by using the covariance-primarily based formula. For considered one of your securities, draw a horizontal line on the chart connecting the safety threat return point to the CML to demonstrate the translation of beta as a "weight" in a similar systematic danger mini-portfolio made up of the risk-loose asset and the Tangent Portfolio. Chart the Security Market Line that relates beta to return for all four securities and the Tangent portfolio. This chart indicates that with overall foresight of the dangers and returns the CAPM formula holds with the careful desire of Tangent Portfolio. What is the that means of the slope of the SML in this chart? What happens to this figure if the tangent portfolio isn't always selected just right? Next, we can use the following two years of records that we "held back" to look how the CAPM performs at pertaining to individual security returns to "marketplace" returns. Use the actual subsequent-two-yr Tangent Portfolio return (we are looking into the destiny with this piece). Use the CAPM components (with Tangent Portfolio taking the function of Market Portfolio) to estimate the go back for each safety. Keep the betas and TP weights discovered from the earlier statistics. Recreate the same two charts (SML and CML) to have a look at within the first one which the TP is no longer pretty most excellent. For the SML chart include the CAPM forecasts as well as the real returns. The CAPM does now not perfectly are expecting forward returns. The market may want to have had pricing mistakes. The cash flow forecasts for the securities might have changed. There is idiosyncratic return each up and down. More realistically, we'd not actually have foresight of the TP returns anyway. What is the CAPM for?

Detailed Instructions (Each of these is a step to do, no longer a component to hand in)

1. Choose 4 actual securities and accumulate 5 years of monthly trading records for them.

A. Use Yahoo finance, ancient statistics

b. Pick securities with reasonable high quality returns, not too hot. Pick things which can be rather diversifying, i.E. One-of-a-kind from every other. Stocks are top thoughts, however also perhaps a bond ETF or Gold or BTC for the ones fans (For BTC, I divided all returns through four to make it paintings).

C. Select month-to-month, 5 years

d. Download to Excel

e. Yahoo adjusts for dividends (and splits) so that you can forget about dividends. Also ignore open and near charges. F. Compute monthly returns on the "adj near" column: Return1 = P1/P0 - 1 g. Paste this column for all of your securities into one excel table

2. In records science it is not unusual to educate a version on a first set of information, then test it on the second set. Using best the primary three years of statistics, chart the danger-return profile of each security in addition to a ramification of fixed-weight portfolios created from the ingredients.

A. Use the formulation STDEV and AVERAGE

b. Since the information is monthly, you may annualize through multiplying by 12 for the returns and multiplying by using sqrt(12) for the threat. (Basically, the variance grows through a thing of 12, however Stdev is rectangular root of variance). Put these summary information above the records where you can see it.

C. Remember to most effective use the first 3 years of records

d. We will make a brand new column for blends of those month-to-month returns. Each month is a made of the returns and weights. Use SUMPRODUCT or MMULT. These are the equal aspect except for how the facts is coated up, I observed MMULT beneficial. The idea is that we rebalance each month to the fixed weights, then get the resulting blended return each month.

E. Do 10-15 of these with diverse weights. Just like the person securities, you may calculate hazard and go back.

F. Chart the risk vs go back for the securities and mixed portfolios. Label the chart.

Q4) Please briefly explain the trade-off for fragmentation of the packets into smaller or bigger packets. Q5) Using the Closest Shortest Path First routing algorithm, if we have the constraint of having minimum 90 kbps link speed, which path should be foloowed from node A to node F? 150 Mbp : band wid - 100 Mbps 150 Mbp$ 1 50 Mb ps D E A 2 F 150 Mb p# 100 Mbps 150 Mbp: G 90 Mbps ICO Mbp# 150 H 100 MbpsQuestion 2: (9 Marks) A broker is trading his money in the stock market. Assume that the daily price of a specific stock along a certain period of time is given as follows: Price [200, 500, 800, 100, 300, 50] all in $. This means that the price of the stock is $200 in the first day, $500 in the second day, and so on. You are allowed to buy and sell the stock only once, which means that if you buy it on the 13 day (i.e. $200) and then sell it on the 3'd day (i.e. $800) a profit of $600 will be gained. You are requested to develop an algorithm to maximize the profit in single buy and sell. Another example: int prices = {300, 450, 720, 90, 30, 50, 900, 500, 70}; Output: Term Buying date: day 5, at the price of 30$ Term selling date: day 7, at the price of 900$ BUY Maximum Profit: 870$ Answer the following questions: a) Design a brute force algorithm (pseudocode) to solve the above problem (1 mark), and determine its complexity (1 marks). b) Design an efficient algorithm (pseudocode ) to solve the above problem (2 marks), and determine its complexity (1 marks). c) develop a brief report to explain the difference between the two algorithms and explain why one of them is more efficient than the other. (2 marks) d) Implement the efficient algorithm using Python (2 marks)