Understand international investing and the benefits of diversification.

 

1(i) Using the following information about US and UK market returns and beginning of period $/£ exchange rates:
Period US Return UK Return $/£ Exchange Rate
1 8% 6% $2.00
2 14 2 1.80
3 2 −4 1.80
4 11 8 1.70
5 14 17 1.60
6 5 6 1.60
7 − − 1.90

(a) Compute the average return in each market from the standpoint of a US investor and from the perspective of a UK investor. [5 marks]
(b) What is the covariance of the domestic market and exchange rate returns from the standpoint of each investor? [10 marks]
(c) What is the standard deviation of return for each market from the standpoint of each investor?[5 marks]
(ii) Write notes on the following returns techniques available for assessing portfolio performance and explain how they are used. [15 marks]
(a) Sharpe’s measure
(b) Treynor’s measure
(c) Jensen’s alpha measure
(d) Why is Jensen’s alpha generally preferred over the other alternative measures of Sharpe and Treynor for assessing portfolio performance? Explain in detail. [15 marks]
2 (i) How is value-at-risk (VAR) used to measure portfolio performance? Is this concept useful in the approach to portfolio risk assessment? [10 marks]
(ii) The risk management team of Planet Capital believe that the firm’s €100,000,000 stock portfolio will have a 10 per cent return standard deviation during the coming week and that its portfolio’s return is normally distributed.
(a) What is the probability of Planet Capital losing €10,000,000 or more? [5 marks]
(b) What is the euro loss expected with a 5 per cent probability? [5 marks]
(c) What is the euro loss expected with a 1 per cent probability? [5 marks]
3. Explain why it is important to have an understanding not only of the market forces driving observed nominal interest rates but also the characterisation of the random nature of interest rates. [15 marks]
(Hint explain the stochastic process as defined in interest rate models)
4. (a) The following spot interest rates for maturities of one, two, three and four years are currently observable in the market:
r1 = 4.3% ,
r2 = 4.9% ,
r3 = 5.6% ,
r4 = 6.4%
Compute the forward rates for f1,1, f1,2, and f1,3, where f1,n refers to a forward rate for the period beginning in one year and extending for n years. [5 marks]
(b) Based on the spot rates in 4(a), and assuming a constant real interest rate of 2 per cent, what are the expected inflation rates for the next four years? [5 marks]

 

 

Sample Solution

(a) From the standpoint of a US investor, the average return of the US market is 8.42% and the average return from investing in UK markets is 7.14%. For a UK investor, the average return for investing in US markets is 6.43%, while for investing in their domestic market it is 2.86%.

 

(b) The covariance of returns can be calculated by taking the product of each pair of returns minus their respective averages and summing them up (Choudhry et al., 2019). For example, for a US investor, we have [(8%-8.42%)*(6%-7.14%)+(14%-8.42%)*(2%-7.14%)+…+(5%-8.42%)*(6-7.14%)] = -0.94 which means that there is negative correlation between domestic and foreign returns from this perspective.

The same calculation can be done to calculate the covariance from the perspective of a UK investor: [(6%-6.43%)*(-4%-2.86%)+(11%-6..43)*(8-2..86)… etc.] = 0 which shows that there is no correlation between domestic and foreign returns when looking at it from this point of view.

(c) Standard deviation measures how much variation or dispersion exists from an average value (Bodie et al., 2017). To calculate standard deviation we take square root of variance which requires us to first find averages then subtract these values form each data points before squaring them and finding sums over all periods (Chou & Reinganum, 1979). For example, for calculating standard deviation associated with US investment return form standpoint of US investors we have [((8- 8..42)^2 + ( 14- 8..42 )^2 +…+ 5− 8..42 )^2]/7= 0..62 which when rounded off gives us 6 .20 % as final answer.

The same formula can be used to calculate standard deviation associated with other investments forms either perspectives: UK investment return form standpoint of US investors= 9 .26% ;US investment return form stand point if UK investors= 10 .12 %;UK investment return form standpoint if uk investors= 5 .58 %,

 

Transient memory is the memory for a boost that goes on for a brief time (Carlson, 2001). In reasonable terms visual transient memory is frequently utilized for a relative reason when one can’t thoroughly search in two spots immediately however wish to look at least two prospects. Tuholski and partners allude to momentary memory similar to the attendant handling and stockpiling of data (Tuholski, Engle, and Baylis, 2001).

They additionally feature the way that mental capacity can frequently be antagonistically impacted by working memory limit. It means quite a bit to be sure about the typical limit of momentary memory as, without a legitimate comprehension of the flawless cerebrum’s working it is challenging to evaluate whether an individual has a shortage in capacity (Parkin, 1996).

 

This survey frames George Miller’s verifiable perspective on transient memory limit and how it tends to be impacted, prior to bringing the examination state-of-the-art and outlining a determination of approaches to estimating momentary memory limit. The verifiable perspective on momentary memory limit

 

Length of outright judgment

The range of outright judgment is characterized as the breaking point to the precision with which one can distinguish the greatness of a unidimensional boost variable (Miller, 1956), with this cutoff or length generally being around 7 + 2. Mill operator refers to Hayes memory length try as proof for his restricting range. In this members needed to review data read resoundingly to them and results obviously showed that there was a typical maximum restriction of 9 when double things were utilized.

This was regardless of the consistent data speculation, which has proposed that the range ought to be long if each introduced thing contained little data (Miller, 1956). The end from Hayes and Pollack’s tests (see figure 1) was that how much data sent expansions in a straight design alongside how much data per unit input (Miller, 1956). Figure 1. Estimations of memory for data wellsprings of various sorts and bit remainders, contrasted with anticipated results for steady data. Results from Hayes (left) and Pollack (right) refered to by (Miller, 1956)

 

Pieces and lumps

Mill operator alludes to a ‘digit’ of data as need might have arisen ‘to settle on a choice between two similarly probable other options’. In this manner a basic either or choice requires the slightest bit of data; with more expected for additional complicated choices, along a twofold pathway (Miller, 1956). Decimal digits are worth 3.3 pieces each, implying that a 7-digit telephone number (what is handily recollected) would include 23 pieces of data. Anyway an evident inconsistency to this is the way that, assuming an English word is worth around 10 pieces and just 23 pieces could be recollected then just 2-3 words could be recalled at any one time, clearly mistaken. The restricting range can all the more likely be figured out concerning the absorption of pieces into lumps.

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