TUNING I Y II

3.1.1 Methodology

This section demonstrates the empirical estimations of firm-level risk measures adopted in this thesis.

Volatility

Volatility of the sampled institutions is obtained from a Generalised AutoRegressive Conditional Heteroskedasticity (GARCH) (1,1) model as shown below. GARCH(1,1) is chosen

because it is simple and best fits financial time series.

@_AM = O_A + Q_AMR_AM, R_AM~T(0,1) (1) Q_AMW _{= X}

A + LA(QAMYZRAMYZ)W+ [ZQAMYZW (2)

where @_AM denotes the equity return of firm i at time t, Q_AM the standard deviation, O_A the expected return, and X_A, L_A, [_Z the parameters. Daily return has been obtained from equity prices, and daily volatility of each sample company is achieved from Eq.1. and Eq.2. Following this, quarterly results are acquired by taking the average values of daily volatility.

VaR

According to the aforementioned definition, VaR is expressed as:

\@(@AM ≤ −()$AM(L)) = L (3)

Where ()$_AM refers to the value of risk of firm i at time t, and L is 0.05. This thesis employs quantile estimation on daily equity price to obtain quarterly values of VaR for each sample company.

Expected Shortfall

ES is defined as the expected loss when losses exceed VaR:

_`_AM = −__MYZ(@_AM|@_AM ≤ −()$_AM(L)) (4)

Following Eq.3 and Eq.4, quarterly VaR is computed first, and quarterly ES is obtained by taking the average of all returns that are no greater than the quarterly VaR.

Beta

Beta is computed according to Eq.5:

[_AM =123(56b,5cb)

=D5(5cb) (5)

where @_dM denotes the market return. "#e(@_AM, @_dM) and ()@(@_dM) are obtained from Dynamic Conditional Correlation (DCC) model (Engle 2002): denote RAM = @AM/QAM and RdM = @dM/QdM

the volatility adjusted returns for @_AM and @_dM respectively. The DCC correlations are thus:

"#@ g_RRAM

dMh = $M = i

1 jAM

j_AM 1 k = l%)m(nAM)YZ/WnAMl%)m(nAM)YZ/W (6)

where n_AM is the pseudo correlation matrix and its dynamics are specified as:

nAM = (1 − L − [)`A + L g R_AMYZ RdMYZh g R_AMYZ RdMYZh o + [nAMYZ (7)

where `A is the unconditional correlation matrix of RAM and RdM. In this thesis, the daily variance

of company returns, and the covariance of company and market returns are achieved from Eq.6. Following this, quarterly variances and covariances are obtained using the mean values of daily ones. Finally, values of beta are the results from Eq.5.

CDS spread is the daily data of 5-year CDS contracts retrieved from Datastream. 5-year maturity is chosen because it is the most liquid type of contract.

Z-Score

Z-Score is defined as the inequality below:

\@($pq ≤ −_q) ≤ rW ₍₈₎ r ≡t>uv(?w>)_x(?w>) (9)

where ROA denotes the return on asset, O($pq) and Q($pq) the mean and standard deviation

of ROA respectively, EA the total equity over asset, and Z the Z-Score. Eq.8 and Eq.9 assume that ROA is normally distributed, however ROAs are normally nonstationary, so this thesis follows the Algorithm 1 in Mare et al. (2016) to estimate Z-Score by considering nonstationary ROA. Specifically, the first step is to fit a trend line y (z) = ) + {z to ROA realisations for each rolling time window. Compute the central value of each trend line and detrend ROA realisations by restoring the differences between ROA realisations and the corresponding central values of certain trend lines (line 5 in Table 2). Then estimate |̅ using the mean value of the central values of the trend lines and the detrended ROA realisations (line7,8,9 in Table 2). The forecasted average ROA values in time t is f(t), and |̅y(~) is ROA standard deviation

when |̅y(~) is big enough, otherwise ROA standard deviation will be obtained from the bias

Table 2 Z-Score Computation for Nonstationary ROA

Algorithm: computing r_F

Data: denote @ an array of ROA realisations; ~ the period to estimate the Z-Score; EA

equity over asset at time ~; k the time window (in periods) used for trend estimation,

an odd number greater than one.

Result: Ä the estimated Z-Score at period ~ 1 Å = ~ − ' − 1; l = {}; Ñ = {}; ' = 1; 2 for% ≤ Å + 1do

3 fit a trend line y (z) = ) + {z to the time series @_A, … , @_AuFYZ;

4 Ñ = Ñ⋃{y(% + (' − 1)/2)};

5 l = l⋃{@_Au(FYZ)/W− y(% + (' − 1)/2)};

6 end

7 â = âä)Å(Ñ);

8 & = &~)Ål)@l läe%)~%#Å (l); 9 |̅ = (1 + 1/(4(n + 1)))s/m; 10 if||̅y(~)| ≤ Rthen

11 standard deviation forecast very close to zero, i.e., smaller than R;

12 &̅ = &é̅(Å + 1)/√Å;

13 Ä = −(_q + y(~))/&̅;

14 else

15 Ä = −(_q + y(~))/(|̅y(~));

16 end

By comparing the sector risk analyses of the firm-level risk measures using various data, the first hypothesis that this section attempts to test is as below.

H3.1: Sector risk ranking varies depending upon the particular data type that a firm-level risk is based on.

Considering that Standard & Poor’s employs CDS as early risk warning signals of outliers that may require imperative review, this section tests the second hypothesis below by comparing the results of CDS spread with those of other data-based risk measures, as well as by testing structural breaks of the firm-level risk measures.

H3.2: CDS spread provides early risk signals than equity-based and accounting-based firm- level risk metrics.

3.1.2 Data

All data in this thesis – equity prices, CDS spread, market values, book value of assets, book value of equity, book value of debt, are retrieved from Datastream. Among them, equity prices, CDS spread, and market values are daily data ranging from 3/1/2005 to 31/12/2014, while book value of assets, book value of equity, and book value of debt are quarterly data from Q1 2005 and Q4 2014. 2005 is the earliest time to be included in a pre-crisis analysis in that CDS data is only available since 2005. In addition, this thesis focuses on risk level changes between the pre-crisis period and crisis period, therefore the post-crisis period in this thesis do not include the latest years and ends in 2014. Companies are classified according to Standard Industrial Classification (SIC) codes: 6000-6199 (banks), and 6300 to 6499 (insurers). Non-financial institutions are selected from the non-financial compositions of S&P 500 by market value. Due to the limitation of CDS data, and in order to achieve an equal company number within each industry, sample size in this thesis is 96, with 32 banks, 32 insurers, and 32 non-financial institutions. In each industry, companies are selected depending on whether they have valid CDS data, on top of which only the largest companies (measured by market value) are included. Data requirements for the firm-level risk measures employed in this thesis are listed in Table 3, where _q = êëD5Mí5ìî ï22F tñëAMî_{êëD5Mí5ìî ó2MDì >òòíM} and $pq =_{êëD5Mí5ìî ó2MDì >òòíM}êëD5Mí5ìî ?íMë5E .

Table 3 Data Requirements of Firm-Level Risk Measures

Firm-level risk measures Data Data type Frequency Sample

Volatility Equity return Market Daily 3/1/2005–31/12/2014

VaR Equity return Market Daily 3/1/2005–31/12/2014

Expected Shortfall Equity return Market Daily 3/1/2005–31/12/2014

Beta Equity return,

market return

Market Daily 3/1/2005–31/12/2014

CDS spread CDS spread Market Daily 3/1/2005–31/12/2014

Z-Score EA, ROA Accounting Quarterly 2005 Q1 – 2014 Q4

Source: Datastream

Both the aforementioned firm-level risk measures and the systemic risk measures in Section 4 are applied to banks, insurers and non-financial institutions (NFIs) across regions including U.S., Europe and Asia. Due to the limitation of CDS data, sample size is confined to 96 companies with each industry comprising 32 firms. However, all the companies in each sector are selected from the S&P 500 index components in a descending order by market capitalisation, and thus they are the largest ones on which CDS contracts are written in a specific industry. The list of the 96 companies is presented in Appendix 1. If a company has subsidiaries, only the holding company is selected, assuming that the risk level of a parent corporation affects and represents the instability of its subsidiaries.

Appendices from Appendix 2 to Appendix 5 have described the statistics of CDS spread and equity returns by company and by sector respectively. Sample period spans from 3rd January 2005 to 31st December 2014, thus there are 2608 CDS observations and 2607 equity returns for each institution. In Appendix 2, firms with maximum CDS values exceeding 1000 are in bold: AIG, Legal & General, Lincoln National, MBIA, MGIC, Metlife, Morgan Stanley, Old Mutual, Radian Group and The Hartford. On the other hand, companies are highlighted with minimum equity returns lower than -0.39 in Appendix 4: AIG, Aviva, CNA Financial, Citigroup, Lincoln National, Lloyds Banking Group, MBIA, MGIC, RBS and The Hartford. Appendix 3 shows that the insurance sector is the riskiest sector with the highest CDS spreads in terms of mean, standard deviation and maximum values. In Appendix 5, the banking industry is associated with the largest losses with the lowest mean and minimum value of equity returns, while the equity returns of insurance companies are volatile the most indicated by standard deviation. Appendix 6 and Appendix 7 have presented the statistical descriptions of equity over asset (EA) and return on asset (ROA). Since EA and ROA are computed from balance sheet data, they are on quarterly basis with sample period ranging from 2005 Q1 to 2014 Q4, i.e. 40 observations. In terms of mean values in Appendix 6 and Appendix 7, both EA and ROA of NFIs are higher than those numbers of insurers and banks.