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Value at Risk The New Benchmark for Managing Financial Risk 3rd edition Philippe Jorion - Solutions
On a system with paging, a process cannot access memory that it does not own; why? How could the operating system allow access to other memory?Why should it or should it not?
Compare paging with segmentation with respect to the amount of memory required by the address translation structures in order to convert virtual addresses to physical addresses.
Program binaries in many systems are typically structured as follows. Code is stored starting with a small fixed virtual address such as 0. The code segment is followed by the data segment that is used for storing the program variables. When the program starts executing, the stack is allocated at
Consider a paging system with the page table stored in memory. a. If a memory reference takes 200 nanoseconds, how long does a paged memory reference take? b. If we add associative registers, and 75 percent of all page-table references are found in the associative registers, what is the effective
A risk manager wants to assess the risk of a hedge fund. The fund is concentrated in a few stocks and is market-neutral (in other words, it has zero beta). Under these conditions, is it appropriate to use a one- factor market model?
Factor analysis reduces correlations to interactions between a small number of risk factors. For fixed-income portfolios, the number of factors should be two, irrespective of the portfolio. Discuss.
A portfolio manager invests in the U.S. and euro bond markets. Returns are measured in dollars. How many important factors are likely to show up in a principal components analysis applied to these markets?
Can copulas be used to model nonlinear correlation coefficients?
Consider the following covariance matrix: (a) Is this positive definite? (b) What is the meaning of a unit correlation coefficient? (c) Can we come up with a vector of positions that will create zero risk?
Consider two stocks with the following decomposition on the market index:The volatility of the market index is 0.15. Compute the covariance matrix using the diagonal and beta models. What is the correlation between the stocks?
The factor model behind the driver for asset correlations under Basel II is Ri = √0.2Rm + √1 - 0.2∈i,-, where the volatility of Rm and ∈ is 1; the residuals e are uncorrelated across assets. Compute the correlation between any two assets.
Using data from section 8.2.4, compute the one-factor and two-factor VAR measures for the portfolios: (a) $100 million in the 5-year bonds and $100 million in the 10-year bonds (b) Short $170 million in the 5-year bonds and long $100 million in the 10-year bonds. Comment on the results.
Give an example that illustrates the problem with restarting the block move instruction (MVC) on the IBM 360/370 when the source and destination regions are overlapping.
Consider a demand-paging system with the following time-measured utilizations:CPU utilization.................. 20%Paging disk....................... 97.7%Other I/O devices............... 5%Which (if any) of the following will (probably) improve CPU utilization? Explain your answer.a. Install
Suppose that a machine provides instructions that can access memory locations using the one-level indirect addressing scheme. What is the sequence of page faults incurred when all of the pages of a program are currently non-resident and the first instruction of the program is an indirect memory
Suppose that your replacement policy (in a paged system) is to examine each page regularly and to discarding that page if it has not been used since the last examination. What would you gain and what would you lose by using this policy rather than LRU or second-chance replacement?
A page-replacement algorithm should minimize the number of page faults. We can do this minimization by distributing heavily used pages evenly over all of memory, rather than having them compete for a small number of page frames. We can associate with each page frame a counter of the number of pages
Consider a demand-paging system with a paging disk that has an average access and transfer time of 20milliseconds.Addresses are translated through a page table in main memory, with an access time of 1microsecond per memory access. Thus, each memory reference through the page table takes two
What is the cause of thrashing? How does the system detect thrashing? Once it detects thrashing, what can the system do to eliminate this problem?
Is it possible for a process to have two working sets? One representing data and another representing code? Explain.
Consider the parameter ∆ used to define the working-set window in the working-set model. What is the effect of setting ∆ to a small value on the page fault frequency and the number of active (non-suspended) processes currently executing in the system? What is the effect when ∆ is set to a
Assume there is an initial 1024 KB segment where memory is allocated using the Buddy System. Using Figure 9.27 as a guide, draw the tree illustrating how the following memory requests are allocated: • Request 240 bytes • Request 120 bytes • Request 60 bytes • Request 130 bytes Next, modify
The slab allocation algorithm uses a separate cache for each different object type. Assuming there is one cache per object type, explain why this doesn't scale well with multiple CPUs. What could be done to address this scalability issue?
Discuss the hardware support required to support demand paging.
Consider a system that allocates pages of different sizes to its processes. What are the advantages of such a paging scheme? What modifications to the virtual memory system are provide this functionality?
What is the copy-on-write feature and under what circumstances is it beneficial to use this feature? What is the hardware support required to implement this feature?
A certain computer provides its users with a virtual-memory space of 232 bytes. The computer has 218 bytes of physical memory. The virtual memory is implemented by paging, and the page size is 4096 bytes. A user process generates the virtual address 11123456. Explain how the system establishes the
Assume we have a demand-paged memory. The page table is held in registers. It takes 8 milliseconds to service a page fault if an empty page is available or the replaced page is not modified, and 20 milliseconds if the replaced page is modified. Memory access time is 100 nanoseconds. Assume that the
Assume that you are monitoring the rate at which the pointer in the clock algorithm (which indicates the candidate page for replacement) moves. What can you say about the system if you notice the following behavior: a. Pointer is moving fast b. Pointer is moving slow
Discuss situations under which the least frequently used page-replacement algorithm generates fewer page faults than the least recently used page replacement algorithm. Also discuss under what circumstance does the opposite holds.
Discuss situations under which the most frequently used page-replacement algorithm generates fewer page faults than the least recently used page replacement algorithm. Also discuss under what circumstance does the opposite holds.
The VAX/VMS system uses a FIFO replacement algorithm for resident pages and a free-frame pool of recently used pages. Assume that the free-frame pool is managed using the least recently used replacement policy. Answer the following questions:a. If a page fault occurs and if the page does not exist
In practice, we seem to observe too many extreme observations than warranted by the normal distribution. Give two explanations for this observation.
For the EWMA model with decay of 0.94, the number of effective observations is said to be small. Explain.
The current estimate of daily volatility is 1 percent. The latest return is 2 percent. Using the EWMA model with A = 0.94, compute the updated estimate of volatility.
Why is the general GARCH model not used commonly to model the full covariance matrix?
Explain why we need to bother about modeling the joint distribution of N risk factors. Given the problems created by the dimensionality that increases with the square of N, it would seem simpler to apply univariate GARCH to the current portfolio only.
What is the advantage of using ISD (implied standard deviation) to predict volatility?
The moving average is one approach to estimate volatility. List two drawbacks to this method.
Consider a file system where a file can be deleted and its disk space reclaimed while links to that file still exist. What problems may occur if a new file is created in the same storage area or with the same absolute path name? How can these problems be avoided?
Discuss the advantages and disadvantages of associating with remote file systems (stored on file servers) a different set of failure semantics from that associated with local file systems.
What are the implications of supporting UNIXc onsistency semantics for shared access for those files that are stored on remote file systems.
The open-file table is used to maintain information about files that are currently open. Should the operating system maintain a separate table for each user or just maintain one table that contains references to files that are being accessed by all users at the current time? If the same file is
What are the advantages and disadvantages of a system providing mandatory locks instead of providing advisory locks whose usage is left to the users' discretion?
What are the advantages and disadvantages of recording the name of the creating program with the file's attributes (as is done in the Macintosh Operating System)?
Some systems automatically open a file when it is referenced for the first time, and close the file when the job terminates. Discuss the advantages and disadvantages of this scheme as compared to the more traditional one, where the user has to open and close the file explicitly.
If the operating system were to know that a certain application is going to access the file data in a sequential manner, how could it exploit this information to improve performance?
Give an example of an application that could benefit from operating system support for random access to indexed files.
Discuss the merits and demerits of supporting links to files that cross mount points (that is, the file link refers to a file that is stored in a different volume).
Some systems provide file sharing by maintaining a single copy of a file; other systems maintain several copies, one for each of the users sharing the file. Discuss the relative merits of each approach.
Discuss the basic tradeoffs between cost, speed, and accuracy when choosing a VAR method. Which method is the fastest? Which has highest accuracy?
Suppose that an investor is long a call option on a stock index futures contract. Each option gives the right to purchase one unit of the index, which is priced at S = $400. The delta is 0.569, and the gamma is 0.010. If the volatility of the rate of return on the index is 30 percent, what is the
As a risk manager, you are asked to design a system to measure the risk of a portfolio of forward contracts on foreign currencies. The trader insists that he should have intraday VAR measures at the 95 percent confidence level. Which method should you choose?
Is the following statement true? Explain why or why not. "Computing VAR with a full-valuation method is feasible with two-function valuations when the payoff function is monotonic."
A risk manager has implemented a GARCH model that indicates that the current volatility is twice the historical average over the last 4 years used for historical simulation. How can this information be taken into account?
Consider a file system that uses a modifed contiguous-allocation scheme with support for extents. A file is a collection of extents, with each extent corresponding to a contiguous set of blocks. A key issue in such systems is the degree of variability in the size of the extents. What are the
Explain why logging metadata updates ensures recovery of a file system after a file system crash.
Consider the following backup scheme: • Day 1. Copy to a backup medium all files from the disk. • Day 2. Copy to another medium all files changed since day 1. • Day 3. Copy to another medium all files changed since day 1. This contrasts to the schedule given in Section 11.7.2 by having all
What are the advantages of the variation of linked allocation that uses a FAT to chain together the blocks of a file?
Consider a system where free space is kept in a free-space list. a. Suppose that the pointer to the free-space list is lost. Can the system reconstruct the free-space list? Explain your answer. b. Consider a file system similar to the one used by UNIX with indexed allocation. How many disk I/O
Some file systems allow disk storage to be allocated at different levels of granularity. For instance, a file system could allocate 4 KB of disk space as a single 4-KB block or as eight 512-byte blocks. How could we take advantage of this flexibility to improve performance? What modifications would
Discuss how performance optimizations for file systems might result in difficulties in maintaining the consistency of the systems in the event of computer crashes.
Consider a file system on a disk that has both logical and physical block sizes of 512 bytes. Assume that the information about each file is already in memory. For each of the three allocation strategies (contiguous, linked, and indexed), answer these questions:a. How is the logical-to-physical
Fragmentation on a storage device could be eliminated by recompaction of the information. Typical disk devices do not have relocation or base registers (such as are used when memory is to be compacted), so how can we relocate files? Give three reasons why recompacting and relocation of files often
Consider the following augmentation of a remote-file-access protocol. Each client maintains a name cache that caches translations from file names to corresponding file handles. What issues should we take into account in implementing the name cache?
A portfolio manager holds a $100 million price position in 10-year Treasury notes with a daily volatility of 0.9 percent. The manager can hedge by selling 5-year T-notes with a daily volatility of 0.5 percent and correlation of 0.97. For computation of VAR, assume normal distributions and a 95
A U.S. exporter sold forward Y125 million at the 7-month forward rate of Y124.27/$. Immediately after the deal is signed, the spot rate moves from Y125 to Y130/$. Dollar and yen rates are still at 6 and 5 percent, respectively. What is the gain/loss of the contract?
Consider a 3-year zero-coupon bond with a face value of $100 and a yield of 4% (annually compounded). Compute this bond's modified duration, dollar duration, and DVBP.
A portfolio manager enters a 10-year pay-fixed swap with notional of $100 million. The duration of the fixed leg is 7.44 years, and the floating leg is about to be reset. Assume a flat term structure and an annual volatility of yield changes of 100 basis points. What is the 95 percent VAR over the
None of the disk-scheduling disciplines, except FCFS, is truly fair (starvation may occur).a. Explain why this assertion is true.b. Describe a way to modify algorithms such as SCAN to ensure fairness.c. Explain why fairness is an important goal in a time-sharing system.d. Give three or more
Compare the throughput achieved by a RAID Level 5 organization with that achieved by a RAID Level 1 organization for the following: a. Read operations on single blocks b. Read operations on multiple contiguous blocks
Compare the performance of write operations achieved by a RAID Level 5 organization with that achieved by a RAID Level 1 organization.
Assume that you have a mixed configuration comprising disks organized as RAID Level 1 and as RAID Level 5 disks. Assume that the system has flexibility in deciding which disk organization to use for storing a particular file. Which files should be stored in the RAID Level 1 disks and which in the
Is there any way to implement truly stable storage? Explain your answer.
The reliability of a hard-disk drive is typically described in terms of a quantity called mean time between failures (MTBF). Although this quantity is called a "time," the MTBF actually is measured in drive-hours per failure.a. If a disk farm contains 1000 drives, each of which has a 750,000 hour
Discuss the relative advantages and disadvantages of sector sparing and sector slipping.
Discuss the reasons why the operating system might require accurate information on how blocks are stored on a disk. How could the operating system improve file system performance with this knowledge?
The operating system generally treats removable disks as shared file systems but assigns a tape drive to only one application at a time. Give three reasons that could explain this difference in treatment of disks and tapes. Describe additional features that would be required of the operating system
What would be the effect on cost and performance if tape storage were to achieve the same areal density as disk storage? (Areal density is the number of gigabits per square inch.)
You can use simple estimates to compare the cost and performance of a terabyte storage system made entirely from disks with one that incorporates tertiary storage. Suppose that magnetic disks each hold 10 gigabytes, cost $1000, transfer 5 megabytes per second, and have an average access latency of
Suppose that a disk drive has 5000 cylinders, numbered 0 to 4999. The drive is currently serving a request at cylinder 143, and the previous request was at cylinder 125. The queue of pending requests, in FIFO order, is 86, 1470, 913, 1774, 948, 1509, 1022, 1750, 130 Starting from the current head
Imagine that a holographic storage drive has been invented. Suppose that a holographic drive costs $10,000 and has an average access time of 40 milliseconds. Suppose that it uses a $100 cartridge the size of a CD. This cartridge holds 40,000 images, and each image is a square black-and-white
Suppose that a one-sided 5.25-inch optical-disk cartridge has an areal density of 1 gigabit per square inch. Suppose that a magnetic tape has an areal density of 20 megabits per square inch, and is 1/2 inchwide and 1800 feet long. Calculate an estimate of the storage capacities of these two kinds
Discuss how an operating system could maintain a free-space list for a tape-resident file system. Assume that the tape technology is append only, and that it uses the EOT mark and locate, space, and read position commands as described in Section 12.9.2.1.
From elementary physics, we know that when an object is subjected to a constant acceleration a, the relationship between distance d and time t is given by d = 1/2 at2. Suppose that, during a seek, the disk in Exercise 12.2 accelerates the disk arm at a constant rate for the first half of the seek,
Suppose that the disk in Exercise 12.3 rotates at 7200 RPM. a. What is the average rotational latency of this disk drive? b. What seek distance can be covered in the time that you found for part a?
Requests are not usually uniformly distributed. For example, a cylinder containing the file system FAT or inodes can be expected to be accessed more frequently than a cylinder that only contains files. Suppose you know that 50 percent of the requests are for a small, fixed number of cylinders. a.
Could a RAID Level 1 organization achieve better performance for read requests than a RAID Level 0 organization (with non redundant striping of data)? If so, how?
Consider a RAID Level 5 organization comprising five disks, with the parity for sets of four blocks on four disks stored on the fifth disk. How many blocks are accessed in order to perform the following?a. A write of one block of datab. A write of seven continuous blocks of data
Explain why pricing methods use risk-neutral distributions. Does risk measurement need risk-neutral or physical distributions?
A risk manager needs to generate two variables with a correlation of 0.6. Explain how this could be done starting from independent variables. Verify that the final variables have unit volatility.
Explain how equilibrium and no-arbitrage models use the current term structure.
Explain why numerical integration is plagued by the curse of dimensionality and why this is avoided by the Monte Carlo simulation method.
Explain how the inverse transform method could generate draws from a student t distribution.
If the movements in the risk factors have positive autocorrelation from one day to the next, can we bootstrap on the changes in the risk factors?
When multiple interrupts from different devices appear at about the same time, a priority scheme could be used to determine the order in which the interrupts would be serviced. Discuss what issues need to be considered in assigning priorities to different interrupts.
Write (in pseudocode) an implementation of virtual clocks, including the queuing and management of timer requests for the kernel and applications. Assume that the hardware provides three timer channels.
Discuss the advantages and disadvantages of guaranteeing reliable transfer of data between modules in the STREAMS abstraction.
What are the advantages and disadvantages of supporting memory mapped I/O to device control registers?
Consider the following I/O scenarios on a single-user PC.a. A mouse used with a graphical user interfaceb. A tape drive on a multitasking operating system (assume no device preallocation is available)c. A disk drive containing user filesd. A graphics card with direct bus connection, accessible
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