Risk Analysis

Posted: August 26th, 2021

Risk Analysis

Name

Institutional Affiliation

Question 1: SPAN System

Standard Portfolio Analysis of Risk (SPAN)as a method of calculating portfolio risk refers to the operation of determining margin requirements using algorithms for the options and futures. The systemcomputes the likely loss in a set of derivative positions ina portfolio. SPAN sets the calculated value as the initial profit that the firm will pay to the investors. The system, through its algorithm, sets the derivatives’ and financial instruments’ margin and calculated the worst possible one-day change (Golembiovsky et al., 2018). The system further analyzes the losses or gains of each contract in different circumstances. Hence, the SPAN system gives SPAN margin or VaR margin,which is the minimum margin requirement to startmarket trading.

The options and futures investorsshould have a minimum amount of margin in hand or their accounts to shield any potential losses. Thus, the SPAN system is used in risk array analysis that calculates the gains or losses of each contract on different conditions knownas risk scenarios. In this case, profits or gains are measured according to price fluctuations in response tovolatilities, following price and volatility changes, as well as a declined expiration time.Various models are used to compute the system, namely: risk-free interest rates, strike prices, volatility change, underlying securities price variations, and time to expiration (Yang, 2018). Therefore, the obtained margins can help to either adjust excess margin on the current position to new positions or upgrade current positions with little margin (analysis on excel work sheet).

            Based on the above background, the following portfolio is considered for analysis:

• 1 long future contract
• 2 short put options to the futures with time to maturity of 3 months and strike at 105% of the SP 500 level
• 1 long call option for the futures with time to maturity of 5 months and strike at 90% of the SP 500 level

The analysis reveals that, without netting the expected margin is 2.15% and 0.102% with netting for the portfolio. The difference is attributed to the fact that netting allows setting off of negative and positive values thus resulting in a low score in the final margin unlike when netting is not used.

Question 2: Stock Analysis

The standard deviation of a portfolio gives portfolio riskand covariance. It also considersthe correlation between financial assets. As such, volatility is used to measure the risk of a stock. In this case, the higher the volatility, the higher the risk, and vice versa, when the risk is low (Manela, 2017). The volatility of a portfolio measures how all the stock values appreciate or decline.

In this assessment, the data analysis is for four companies that include; Intel, JP Morgan, Apple, and Microsoft. The analysis of the individual stocks of the four companies is performed and results discussed below;

Question 2 (part 1). Statistical Analysis of Stock Portfolio

Descriptive and frequency analysis was performed to ascertain the individual characteristics of the portfolio of a combined stock. Table 1 shows the results of the analysis;

Table 1: Descriptive Statistics

Statistics
	Intel	JPMorgan	Apple	Microsoft
N	Valid	1509	1509	1509	1509
Missing	0	0	0	0
Mean	$38.9905	$83.9668	$143.9951	$74.5671
Median	$35.8040a	$84.4000a	$129.2700a	$62.6400a
Mode	$24.76b	$63.60	$97.34b	$62.30
Std. Deviation	$8.98930	$23.52841	$46.65073	$32.58145
Variance	80.808	553.586	2176.290	1061.551
Range	$36.56	$86.07	$220.12	$123.98
Minimum	$23.52	$53.07	$71.40	$34.98
Maximum	$60.08	$139.14	$291.52	$158.96
Sum	$58,836.64	$126,705.89	$217,288.56	$112,521.72
Percentiles	25	$32.3537c	$61.3717c	$107.8950c	$47.0030c
50	$35.8040	$84.4000	$129.2700	$62.6400
75	$47.0450	$107.3600	$175.8275	$101.0675
a. Calculated from grouped data. b. Multiple modes exist. The smallest value is shown c. Percentiles are calculated from grouped data.

Table 1 is a descriptive statistical analysis of the four stocks. The vital statistics include standard deviation, mean, and variance. As reported in the investigation, Apple stocks have the highest mean price of $ 143.995 across the capitals, followed by JPMorgan at $ 83.97. Intel stocks report the lowest mean price of $ 38.99. Subsequently, Apple prices have the highest fluctuations, as shown in standard deviation, with a score of $ 46.95 compared to all other stocks. Intel reports the lowest deviation score of $ 8.0. The smallest and highest prices as depicted by minimum and maximum variation show Intel at $ 23.52 low and $ 60.08 high, JPMorgan at $ 53.07 low, and $ 139.14 high, Apple at $ 71.40 low and $ 291.52 high while Microsoft at $ 34.98 level and $ 158.96 high. Thus, although Apple has the potential to fetch high returns, it has a high risk potential to affect the performance of the portfolio. The results show that the portfolio has the potential to exhibit a balanced and profitable performance as demonstrated by the closing values of each stock for the five years from January 1, 2014- December 31, 2019.

Question 2 (part 2& 3). Estimation of Value at Risk (VaR)

Value at Risk (VaR) estimates the values that may be lost the stock trading and the probability of such risk occurring. The following table shows the VaR results for the portfolio based on 95% and 99% confidence levels.

Table 2: Value at Risk (VaR) Analysis

	Intel	JPMorgan	Apple	Microsoft
Mean Return	$0.00060	$0.00072	$0.00094	$0.00106
STDEV of Returns	0.01618	0.013092497	0.01542	0.014451
VaR (95%)	-2.6%	-2.1%	-2.4%	-2.3%
VaR (99%)	-3.7%	-3.0%	-3.5%	-3.3%

            From the table, at a 95% confidence interval, the maximum losses are 2.6%, 2.1%, 2.4%, and 2.3% for Intel, JPMorgan and Apple, and Microsoft stocks, respectively. At 99%, maximum losses would be 3.9%, 3.0%, 3.5%, and 3.3% for Intel, JPMorgan, Apple, and Microsoft, respectively. Figures 1 and 2 are the summary models used in the analysis:

Figure 1: VaR Model, p = 0.05

Figure 2: VaR Model, p = 0.01

Question 2 (part 4). Kupec Test (Completed on excel)

            Compared to model 1, p=0.05%, model 2, p=0.01 exhibits more failures throughout the period. Hence, the correct model is p = 0.05%.

Question 2 (part 4). Serial Dependence

            The results of serial dependence return a positive correlation of 2.3, implying that serial relationship exists. The calculations are done using excel VAR and COVAR formulas. Hence, do not reject the null hypothesis that serial dependence exists in the occurrence of the violation.

Question 2 (part 5). Marginal and Component VaR (99%-1)

            The following table shows results for marginal and component VaR (99%-1)

Table 3: Marginal and Component VaR

Statistic	Intel	JPMorgan	Apple	Microsoft
Marginal VaR	0.0357	0.0289	0.0338	0.0315
VaR (99%)	-0.0370	-0.0297	-0.0349	-0.0326
Component VaR	0.9364

             Based on the results, the portfolio can be modified by changing the composition of individual stocks, for example, increasing the shares for Intel and reducing Apple stock proportion. Thus, this would minimize risks.

Question 2 (part 6). Minimum Capital Charge

            Based on the risk level as exhibited in the marginal VaR, the minimum capital charge is 0.096.

References

Basak, S., & Atmaz, A. (2018). Options Prices and Costly Short-Selling.

Brooks, R. (2019). Compound Option Valuation with Maturity Varying Volatility, Maturity         Varying Yields, and Maturity Varying Interest Rates. Maturity Varying Yields, and            Maturity Varying Interest Rates (September 23, 2019).

Golembiovsky, Dmitry Jurievich, and Anatoly Markovich Abramov. “Option Portfolio      Management in a Risk-Neutral World.” Journal of Mathematical Finance 8.4 (2018):           710-733.

Manela, A., & Moreira, A. (2017). News implied volatility and disaster concerns. Journal of          Financial Economics, 123(1), 137-162.

Yang, Y. (2018, May). The Statistical Analysis of Implied Parameters for Derivatives Pricing. In 2018 4th International Conference on Humanities and Social Science Research (ICHSSR     2018). Atlantis Press.