Studying The Bankruptcy Of Orange County Finance Essay - Free Essay Example

Sample details Pages: 10 Words: 2920 Downloads: 2 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? The case of bankruptcy of Orange County in 1994 emphasize the importance of using duration and Value at risk (VAR) to assess portfolio risk and avoid future bankruptcy. Duration and VAR analysis provide deeper understanding about the underlying risk of the Orange County Investment Pool which was heavily leveraged and interest-pledged through reverse repurchase agreements and other derivatives in the pool. Some VAR estimation, including historical simulation method, delta-normal method and Monte Carlo simulation will be used to calculate worst possible loss. Don’t waste time! Our writers will create an original "Studying The Bankruptcy Of Orange County Finance Essay" essay for you Create order The EWMA will be used to provide more accurate estimation of the volatility to improve the accuracy of VAR estimation. Background: On Dec 6, 1994, Orange County declared bankruptcy after suffering losses of around $1.6billion from a wrong way bet on interest rates 7.5 billion investment pool. This pool was intended to gain some returns from the investing the money which is raised from taxes and other government incomes. It was implemented a bet that the interest would decline or stay low by Citron (the portfolio manager). Because of the steadily declining interest rates from 1989 to 1992, the portfolio performed extremely well before 1994 and earned millions of above average profit. However, in 1994, the government suddenly declared policies which included raise the interest rates from 3.45% to 7.14% to prevent high inflation and overheating economy. This increase in interest rate caused the portfolio suffer 1.6 billion loss and further lead the bankruptcy of Orange County. Section 1: The heavy leveraged and interest-pledged portfolio In order to sustain above average returns, several investment tools are used by Citron to leverage the $7.5 billion funds into $20.5billion investment. In detail, reverse repurchase agreements allow Citron to use the securities which had already purchased as collateral on further borrowing and then reinvested the cash into new securities (Jameson, 2001). Besides the heavily leveraged risk, the portfolio also encounters significant risk from the unexpected interest movement. Firstly, these repurchase agreements values significantly depend on the change in interest rate. In detail, its value decrease as the interest rate increase and increase as the interest rate decrease (P=). Secondly, $2.8 billion of derivatives, including inverse floating-rate notes, dual index notes, floating-rate notes, index-amortizing notes and collateralized mortgage obligations, are used to increase the portfolio bet on the term structure of the interest rate (Jorion, 2009). Thirdly, median term maturities which had higher yields (5.2%) than the short term investments (3%) were used to increase the return of the portfolio (Jorion, 2009). However, by using longer term maturities, the portfolios sensitivity to interest change will significantly increase. Clearly, by doing these, the portfolios value will be significantly impacted by the movement of the interest. Section 2: Duration of the portfolio and its application Duration of the portfolio Hull (2009) defines the duration as a measure of how long, on average, the holder of the instrument has to wait before receiving cash payments. It measures sensitivity of price changes with changes in interest rates. Duration can be calculated by weighting average (the weight is the proportion of portfolios total present value of cash flow received at time t) of the times. In this case, the portfolio was heavily bet on the interest, therefore, duration might be a good measure for the portfolio. In the $7.5 billion portfolio, median term maturities (5 years), rather than short term maturities (1-3 years), were used to increase the return. By doing this, the duration of the portfolio significant increased. In other words, the portfolio exposed higher risk of interest rate movements. In December 1994, the average duration of the securities in the portfolio was 2.74 years. It means 1% change in interest would cause 2.74% change in portfolios prices. M oreover, Citron leveraged $7.5 billion equity into a $20.5 billion portfolio. This means that a 2.73 leverage ratio (20.5/7.5). In other words, for every dollar of the pool invested, the pool borrowed extra $1.73. For a leveraged portfolio, the effective portfolio duration = ordinary duration * leverage ratio. Thus, the effective portfolio duration of the portfolio is 7.4 (2.74*2.7). Estimation by using duration The response of portfolio prices to change in interest rate: In 1994, the interest rates went up by about 3.5 ( and the 5 years bond yield was 5%, therefore, the loss of the portfolio equals 1.85 (7.5*7.4*3.5%/1.05) which is slightly larger than the actual loss of 1.64 billion. This slightly difference between the loss estimated by duration and the actual loss might be caused by that the duration applies to only small changes in interest rate. As a first order approximation, duration cannot capture the information that two bonds with same duration can have different change in price for large change in interest rate (different convexity). So, convexity (second order approximation) which can capture this information should be added into the estimating model. Through adding this (convexity factor), the estimated loss will slightly less than before, and will more close to the actual loss (1.64 billion). Thus, duration seems to have the ability to accurate measure the portfolios sensitivity to interest rate change. Section 3: Value at risk (VAR) Value at risk (VAR) In order to estimate the underlying risk of the portfolio, VAR which measures the worst expected loss over a given horizon under normal market conditions at a given confidence level could be used (Jorion, 2001). Because the portfolio was heavily bet on the interest rate, its return and risk are significantly depending on the change of interest rate. In other words, the change of interest yield multiplies the modified duration and portfolio value could be used as an approximation of the change of portfolios value. Thus, the change of interest yield could be used in the 3 simulation methods as the only factor that contribute the change of portfolio value. Non-parametric approach (no need to identify variance-covariance matrix) Historical simulation approach The historical simulation accounts for non-linearity, income payments, and even time decay effects through using marking-to-market the whole portfolio over a large number of realizations of underlyi ng random variables. VAR is calculated from the percentiles of the full distribution of payoffs (Jorion, 2001). By using actual price, the method captures Greek risk (gamma, vega risk etc.) and corrections of securities (already exist in the real historical data) in the portfolio, and it does not rely on some specific assumption, such as the underlying stochastic structure of the market (the pre-requests of estimating volatility and mean). Moreover, it can account for fat tails distribution besides normal distributions (Jorion, 2001). (Figure 1) The root-T approach will be used to transfer the monthly VAR to yearly VAR in all the 3 approaches. Its success significantly relies on the some specific assumptions, including the monthly yield changes of the portfolio are identically and independently distributed (iid distribution) and the return has a constant variance (Cuthbertson and Nitzsche, 2001). However, in the real world, stock returns always has time varying variance and th ere are some autocorrelation factors exist (thus, not independent). Therefore, as the T increase, the error of the transformation will significantly increase. The VAR will be calculated through sorting the monthly yield change and picking the worst daily yield change at 5% percentile (see details in CD). However, in this case, the increase in yield will cause decrease in portfolio return, therefore, the worst daily yield change should be picked at the right hand side of the histogram (see figure 1). The VAR equals 1.24 billion annually (0.36 billion monthly) which is less than the actual loss (1.64 billion). This inaccuracy might be caused by the problems exist in historical simulation method. Firstly, the success of the method significantly relies on the assumption that the past price can represent the future price information. However, the assumption is not realistic to some extent because of the existence of market efficient. Secondly, simple historical simulation method may m iss the information of temporarily elevated volatility, such as structural breaks and extreme value (Butler and Schachter, 1996). In this case, the historical simulation method cannot capture the extreme value (1.64 billion loss) which is caused by 6 suddenly decreases of interest rate. Parametric approach (need to need to identify variance-covariance matrix) Delta normal approach The delta normal method is particularly simple approach to implement. It takes account simple variance-covariance matrix and then forecast the total variance of the portfolio (volatility). Then, The VAR can be calculated through the formula: VAR = MD*Portfolio Value*=7.4*7.5*0.4%*1.65/(1.005)=0.35 billion (monthly) = 1.21 billion (annually). Delta normal method is slightly less accurate than the historical in the case. This might caused by that the change in yield does is a fat tail distribution (Kurtosis =6.9, Skewness = -0.44) rather than a normal distribution (Kurtosis =6.9, Skewness = -0.44 ). Thus, the model based on the normal distribution will underestimate the proportion of outliers and hence the value at risk (Jorion, 2001). In addition, the portfolio contains a lot of derivatives instrument. This will cause the method inadequately measures the risk of nonlinearity. Monte Carlo simulation (MCS) (the theoretical most powerful method) Unlike historical simulation, through specifying and stimulating a stochastic process for financial variables, Monte Carlo simulation covers a wide range of financial variables (volatility and stochastic variables) and fully captures correlations of securities (unlike HS, need to define the matrix) in the portfolio (Jorion, 2001). It does not only account for a wide range of risks, such as nonlinear price, volatility and model risks (the same as historical simulation), but also incorporate time variation of volatility (structural breaks and extreme values), and fat tails. Moreover, it can capture the structure changes in the port folio as the time pass (Jorion, 2001). In theoretical way, MCS should be the best method in estimating VAR. The MCS VAR is about 0.295 monthly, through using the root-T rule, the annually VAR is about 1 billion (see detail calculation in CD). There are also some limitations of Monte Carlo simulation cause the estimated error between the estimated loss and actual loss. Its success significantly relies on the specific pricing model for underlying assets and stochastic processes for the underlying risk factors. In this case, the pricing formula is Brownian approach without drift may not accurately capture the actual value change of the portfolio. This might be one possible reason that the estimated loss is not equal to the actual loss. Moreover, the problems may exist in the sample used to derivate the underlying risk factors. For example, MCS will generate less accurate estimates then delta normal method when the risk factors are jointly normal and all payoffs are liner (Cuthbertso n and Nitzsche, 2001). Why MCS (theoretical best method) shows the worst estimation in this case MCS seems to have the least accurate estimation (more closer to the actual loss) in this case. This might be caused by the portfolio used in MCS are treated as one asset which is only impacted by the interest yield. Three factors, including the correlation between all the securities in the portfolio, the underlying risk factors of these securities and the different price formula should be used for each security, are ignored in the powerful approach (Tardivo, 2002). On the other hand, compared with the MCS, historical simulation does not need to define the correlation matrix, because the data has already captured the information. In addition, underlying risk factors also contains in the actual data. Thus, in the case with limited information, historical simulation provides more accurate estimation. Section 4: EWMA In realistic world, the variance of the time series is varying overtime. Thus, the simple unconditional variance (simple variance/standard deviation) may not provide unbiased estimation of the volatility. This will further result in inaccuracy estimation of the VAR. in the case, In the case, the simple variance (volatility) are calculating through assigning the same weight on all observations during Jan 1953 and Dec 1994. This may lead to biased forecasts of VAR because the Fed dramatically increased/decreased the interest rate during this time period. In order to improve the accuracy of estimating VAR, Exponentially weighted moving average (EWMA) will be used to provide more accurate estimation to the volatility at a specific time (conditional standard deviation) (Cuthbertson and Nitzsche, 2001). EWMA method allows more recent observations to have stronger impact on the forecast of volatility than the old observations. In practical way, the recent data are given more weights th an the old data. By applying this model, volatility in practice will be more impacted by recent events and the impacts on volatility will decline as time pass (smaller weights apple to the event) (Brooks, 2002). Through applying the EWMA model, the monthly standard deviation for the six months before December 1994 is 0.348%. The next 6 months volatility could be forecasted through using the formula:. In addition, the actual monthly volatility could use the change in yield as approximation. According to RiskMetrics, the optimalshould be 0.97 (Brock, 2002). ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Forecast volatility (%) Actual volatility (%) Range of the possible volatility at 5% confidence level ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Volatility at june 1994 0.35 ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Left side (-1.65) Right side (1.65) Forecasted volatility ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Jul-94 0.35 -0.26 -0.57 0.57 Aug-94 0.34 0.08 -0.56 0.56 Sep-94 0.35 0.47 -0.57 0.57 Oct-94 0.34 0.20 -0.56 0.56 Nov-94 0.34 0.31 -0.56 0.56 Dec-94 0.34 0.04 -0.55 0.55 Generally, the EWMA approach does not fully capture abnormal volatility change in 1994. In detail, the actual volatility change more volatile than the forecast one (table 1). The inaccuracy involve in estimating the volatility may result in that the calculated VAR is significantly different from the actual possible loss of the portfolio (table 2). If the forecast volatility is used to calculate VAR, manager should aware that the calculated VAR is only an approximation and it cannot capture all the volatility change information. For example, in this case, the actual volatility in Sep-94 is significantly larger than the forecast one. This may cause manager to underestimate the risk in the time period and then holding the portfolio unchanged as before. It is also support by Mahoney (1996) who empirically support that the EWMA volatility has inaccuracy problems. Table 1: ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Forecast volatility (%) Actual volatility (%) Left side (-1.65) Right side (1.65) Volatility at June 1994 0.35 ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Forecasted volatility ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Jul-94 0.35 -0.26 -0.57 0.57 Aug-94 0.34 0.08 -0.56 0.56 Sep-94 0.35 0.47 -0.57 0.57 Oct-94 0.34 0.20 -0.56 0.56 Nov-94 0.34 0.31 -0.56 0.56 Dec-94 0.34 0.04 -0.55 0.55 On the other hand, VAR calculated based on EWMA volatility can still be used as a benchmark to assess the portfolios risk. All of the actual volatility is in the boundary of the forecast volatilitys 5% tail cut off (on both sides *1.65). That is to say, although there are significant differences between the forecast and the actual volatility in this case, portfolio manager may still not underestimate the underlying risk at 5% confidence level (normal distribution). In addition, if better models are used, including GARCH, EGARCH, and GJR , the VAR can provide more precise estimation of the worst possible loss. Table 2: ÃÆ' £Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬ Forecasted VAR(*-1.65) monthly Actual VAR monthly Forecasted VAR annually Actual VAR annually Jul-94 -0.302 0.227 -1.045 0.786 Aug-94 -0.297 -0.070 -1.030 -0.242 Sep-94 -0.301 -0.410 -1.044 -1.420 Oct-94 -0.298 -0.174 -1.034 -0.604 Nov-94 -0.298 -0.270 -1.031 -0.937 Dec-94 -0.293 -0.035 -1.015 -0.121 Section 5: Backtest EWMA model In order to test whether VAR can be used as s a benchmark to assess the portfolios risk, the backtest should be used to test whether EWMA can capture the actual change in interest yield at the 5% left tail cut off level (normal distribution). Practically, if all of the actual changes in interest yield are within the forecast volatilities boundary (the forecast volatility multiply 1.65 at right hand side and -1.65 at the left hand side), the EWMA model can be considered as providing accurate estimation at 5% confidence level. According to figure 2, there are 4 outliers (Aug-89, Jan-92, Feb-94 and Mar-94) are outside the forecast. This will cause manager to over/under estimate the underlying risk of the portfolio. Figure 2: forecast volatilities boundary and actual change in interest yield Section 6: Whether the portfolio should be liquidated in December 1994 Miller and Ross (1997) recommend that the portfolio should not be liquidated until the maturity of the structural notes. This is because after the Orange County bankruptcy, the interest rate fell from 7.8% to 5.25% during Dec 1994 to Dec 1995. If it did not announce the bankruptcy, this decrease in interest rate could help the County to recover 7.4*7.5*2.55%/1.05= 1.32 billion losses. However, the problem is that in Dec 1994, how the managers would know that there would be a decrease in interest in 1995. Jorion (1997) suggest that because it is impossible to predict suddenly interest rate decrease, holding the assets in order to recover value in the next years is speculative and risky. Given this change in yield is a normal distribution, the probability of 2.55% decrease in interest can be calculated through P(=P(-6.223). According to the normal statics table, the probability of such large decrease in interest is less than 1%. Thus, the rational managers would not expect suddenl y large decrease in interest rate. In order to minimize to further loss, it is reasonable to liquidate the portfolio on Dec 1994. In addition, as the portfolio is interest pledged, some interest futures, such as the T-bond futures, could be shorted to hedge the portfolio in Dec 1993. Long cap could also a good choice to generate profit when interest rate exceeds the strike rate. This could partially compensate the massive loss. Conclusion The orange countys heavy leveraged and interest-pledged portfolio suffer massive loss in 1994 because of the suddenly increase of interest rate. Through examining this case study, the Duration and VAR are important measurement of risk to avoid future bankruptcy. Compare the duration estimated loss with the actual loss, Duration (plus convexity) of the portfolio seems to have the ability to accurately measure the portfolios sensitivity to the change in interest rate. In addition, all of the VARs calculated through three approaches, including historical simulation, delta normal, and MCS, are less than the actual loss. The theoretical best approaches (MCS) does not provide the most accurate estimation because of ignorance of some important factors, such as the correlation between all the securities in the portfolio, the underlying risk factors of these securities and the different price formula should be used for each security. The backtest of EWMA (4 outliers) suggest that there are some risk in using VAR to measure the worst possible loss in the real world.

What Is PSI Definition of Unit

PSI definition: PSI is a unit of pressure expressed in pounds of force per square inch of area. It stands for Pounds per Square Inch.1 PSI 6894 Pascals 0.070 atmospheres 51.715 torr

The Crystal Shard 3. The Mead Hall Free Essays

Many miles north of Ten-Towns, across the trackless tundra to the northernmost edge of land in all the Realms, the frosts of winter had already hardened the ground in a white-tipped glaze. There were no mountains or trees to block the cold bite of the relentless eastern wind, carrying the frosty air from Reghed Glacier. The great bergs of the Sea of Moving Ice drifted slowly past, the wind howling off of their high-riding tips in a grim reminder of the coming season. We will write a custom essay sample on The Crystal Shard 3. The Mead Hall or any similar topic only for you Order Now And yet, the nomadic tribes who summered there with the reindeer had not journeyed with the herd’s migration southwest along the coast to the more hospitable sea on the south side of the peninsula. The unwavering flatness of the horizon was broken in one small corner by a solitary encampment, the largest gathering of barbarians this far north in more than a century. To accomodate the leaders of the respective tribes, several deerskin tents had been laid out in a circular pattern, each encompassed in its own ring of campfires. In the center of this circle, a huge deerskin hall had been constructed, designed to hold every warrior of the tribes. The tribesmen called it Hengorot, â€Å"The Mead Hall,† and to the northern barbarians this was a place of reverence, where food and drink were shared in toasts to Tempos, the God of Battle. The fires outside the hall burned low this night, for King Heafstaag and the Tribe of the Elk, the last to arrive, were expected in the camp before moonset. All of the barbarians already in the encampment had assembled in Hengorot and begun the pre-council festivities. Great flagons of mead dotted every table, and good-natured contests of strength sprang up with growing frequency. Though the tribes often warred with each other, in Hengorot all differences were put aside. King Beorg, a robust man with tousled blond locks, a beard fading to white, and lines of experience etched deeply into his tanned face, stood solemnly at the head table. Representing his people, he stood tall and straight, his wide shoulders proudly squared. The barbarians of Icewind Dale stood a full head and more above the average inhabitant of Ten-Towns, sprouting as though to take advantage of the wide and roomy expanses of empty tundra. They were indeed much akin to their land. Like the ground they roamed over, their oftenbearded faces were browned from the sun and cracked by the constant wind, giving them a leathery, toughened appearance, a foreboding, expressionless mask that did not welcome outsiders. They despised the people of Ten-Towns, whom they considered weak wealth-chasers possessed of no spiritual value whatsoever. Yet one of those wealth-chasers stood among them now in their most revered hall of meeting. At Beorg’s side was deBernezan, the dark-haired southerner, the only man in the room who was not born and bred of the barbarian tribes. The mousey deBernezan kept his shoulders defensively hunched as he glanced nervously about the hall. He was well aware that the barbarians were not overly fond of outsiders and that any one of them, even the youngest attendant, could break him in half with a casual flick of his huge hands. â€Å"Hold steady!† Beorg instructed the southerner. â€Å"Tonight you hoist mead flagons with the Tribe of the Wolf. If they sense your fear †¦Ã¢â‚¬  He left the rest unspoken, but deBernezan knew well how the barbarians dealt with weakness. The small man took a steadying deep breath and straightened his shoulders. Yet Beorg, too, was nervous. King Heafstaag was his primary rival on the tundra, commanding a force as dedicated, disciplined, and numerous as his own. Unlike the customary barbarian raids, Beorg’s plan called for the total conquest of Ten-Towns, enslaving the surviving fishermen and living well off of the wealth they harvested from the lakes. Beorg saw an opportunity for his people to abandon their precarious nomadic existence and find a measure of luxury they had never known. Everything now hinged on the assent of Heafstaag, a brutal king interested only in personal glory and triumphant plunder. Even if the victory over Ten-Towns was achieved, Beorg knew that he would eventually have to deal with his rival, who would not easily abandon the fervent bloodlust that had put him in power. That was a bridge the King of the Tribe of the Wolf would have to cross later, the primary issue now was the initial conquest, and if Heafstaag refused to go along, the lesser tribes would split in their alliances among the two. War might be joined as early as the next morning. This would prove devastating to all their people, for even the barbarians who survived the initial battles would be in for a brutal struggle against winter: The reindeer had long since departed for the southern pastures, and the caves along the route had not been stocked in preparation. Heafstaag was a cunning leader; he knew that at this late date the tribes were committed to following the initial plan, but Beorg wondered what terms his rival would impose. Beorg took comfort in the fact that no major conflicts had broken out among the assembled tribes, and this night, when they all met in the common hall, the atmosphere was brotherly and jovial, with every beard in Hengorot lathered in foam. Beorg’s gamble had been that the tribes could be united by a common enemy and the promise of continued prosperity. All had gone well†¦so far. But the brute, Heafstaag, remained the key to it all. * * * The heavy boots of Heafstaag’s column shook the ground beneath their determined march. The huge, one-eyed king himself led the procession, his great, swinging strides indicative of the nomads of the tundra. Intrigued by Beorg’s proposal and wary of winter’s early onset, the rugged king had chosen to march straight through the cold nights, stopping only for short periods of food and rest. Though primarily known for his ferocious proficiency in battle, Heafstaag was a leader who carefully weighed his every move. The impressive march would add to the initial respect given his people by the warriors of the other tribes, and Heafstaag was quick to pounce on any advantage he could get. Not that he expected any trouble at Hengorot. He held Beorg in high respect. Twice before he had met the King of the Tribe of the Wolf on the field of honor with no victory to show for it. If Beorg’s plan was as promising as it initially seemed, Heafstaag would go along, insisting only on an equal share in the leadership with the blond king. He didn’t care for the notion that the tribesmen, once they had conquered the towns, could end their nomadic lifestyle and be contented with a new life trading knucklehead trout, but he was willing to allow Beorg his fantasies if they delivered to him the thrill of battle and easy victory. Let the plunder be taken and warmth secured for the long winter before he changed the original agreement and redistributed the booty. When the lights of the campfires came into view, the column quickened its pace. â€Å"Sing, my proud warriors!† Heafstaag commanded. â€Å"Sing hearty and strong! Let those gathered tremble at the approach of the Tribe of the Elk!† * * * Beorg had an ear cocked for the sound of Heafstaag’s arrival. Knowing well the tactics of his rival, he was not surprised in the least when the first notes of the Song of Tempos rolled in from the night. The blond king reacted at once, leaping onto a table and calling silence to the gathering. â€Å"Harken, men of the north!† he cried. â€Å"Behold the challenge of the song!† Hengorot immediately burst into commotion as the men dashed from their seats and scrambled to join the assembling groups of their respective tribes. Every voice was lifted in the common refrain to the God of Battle, singing of deeds of valor and of glorious deaths on the field of honor. This verse was taught to every barbarian boy from the time he could speak his first words, for the Song of Tempos was actually considered a measure of a tribe’s strength. The only variance in the words from tribe to tribe was the refrain that identified the singers. Here the warriors sang at crescendo pitch, for the challenge of the song was to determine whose call to the God of Battle was most clearly heard by Tempos. Heafstaag led his men right up to the entrance of Hengorot. Inside the hall the calls of the Tribe of the Wolf were obviously drowning out the others, but Heafstaag’s warriors matched the strength of Beorg’s men. One by one, the lesser tribes fell silent under the dominance of the Wolf and the Elk. The challenge dragged on between the two remaining tribes for many more minutes, neither willing to relinquish superiority in the eyes of their deity. Inside the mead hall, men of the beaten tribes nervously put their hands to their weapons. More than one war had erupted on the plains because the challenge of the song could determine no clear winner. Finally, the flap of the tent opened admitting Heafstaag’s standard bearer, a youth, tall and proud, with observing eyes that carefully weighed everything about him and belied his age. He put a whalebone horn to his lips and blew a clear note. Simultaneously, according to tradition, both tribes stopped their singing. The standard bearer walked across the room toward the host king, his eyes never blinking or turning away from Beorg’s imposing visage, though Beorg could see that the youth marked the expressions that were upon him. Heafstaag had chosen his herald well, Beorg thought. â€Å"Good King Beorg,† the standard bearer began when all commotion had ceased, â€Å"and other assembled kings. The Tribe of the Elk asks leave to enter Hengorot and share mead with you, that we might join together in toast to Tempos.† Beorg studied the herald a bit longer, testing to see if he could shake the youth’s composure with an unexpected delay. But the herald did not blink or turn aside his penetrating stare, and the set of his jaw remaining firm and confident. â€Å"Granted† answered Beorg, impressed. â€Å"And well met.† Then he mumbled under his breath, â€Å"A pity that Heafstaag is not possessed of your patience.† â€Å"I announce Heafstaag, King of the Tribe of the Elk.† the herald cried out in a clear voice, â€Å"son of Hrothulf the Strong, son of Angaar the Brave; thrice killer of the great bear; twice conqueror of Termalaine to the south; who slew Raag Doning, King of the Tribe of the Bear in single combat in a single stroke†¦Ã¢â‚¬  (this drawing uneasy shuffles from the Tribe of the Bear, and especially their king, Haalfdane, son of Raag Doning.) The herald went on for many minutes, listing every deed, every honor, every title, accumulated by Heafstaag during his long and illustrious career. As the challenge of the song was competition between the tribes, the listing of titles and feats was a personal competition between men, especially kings, whose valor and strength reflected directly upon their warriors. Beorg had dreaded this moment, for his rival’s list exceeded even his own. He knew that one of the reasons Heafstaag had arrived last was so that his list could be presented to all in attendance, men who had heard Beorg’s own herald in private audience upon their arrival days before. It was the advantage of a host king to have his list read to every tribe in attendance, while the heralds of visiting kings would only speak to the tribes present upon their immediate arrival. By coming in last, and at a time when all the other tribes would be assembled together, Heafstaag had erased that advantage. At length, the standard bearer finished and returned across the hall to hold open the tent flap for his king. Heafstaag strode confidently across Hengorot to face Beorg. If men were impressed with Heafstaag’s list of valor, they were certainly not disappointed by his appearance. The red-bearded king was nearly seven-feet tall, with a barrelshaped girth that dwarfed even Beorg’s. And Heafstaag wore his battle scars proudly. One of his eyes had been torn out by the antlers of a reindeer, and his left hand was hopelessly crumpled from a fight with a polar bear. The King of the Tribe of the Elk had seen more battles than any man on the tundra, and by all appearances he was ready and anxious to fight in many more. The two kings eyed each other sternly, neither blinking or diverting his glance for even a moment. â€Å"The Wolf or the Elk?† Heafstaag asked at length, the proper question after an undecided challenge of the song. Beorg was careful to give the appropriate response. â€Å"Well met and well fought,† he said. â€Å"Let the keen ears of Tempos alone decide, though the god himself will be hard-pressed to make such a choice.† With the formalities properly carried out, the tension eased from Heafstaag’s face. He smiled broadly at his rival. â€Å"Well met, Beorg, King of the Tribe of the Wolf. It does me well to face you and not see my own blood staining the tip of your deadly spear!† Heafstaag’s friendly words caught Beorg by surprise. He couldn’t have hoped for a better start to the war council. He returned the compliment with equal fervor. â€Å"Nor to duck the sure cut of your cruel axe!† The smile abruptly left Heafstaag’s face when he took notice of the dark-haired man at Beorg’s side. â€Å"What right, by valor or by blood, does this weakling southerner have in the mead hall of Tempos?† the red-bearded king demanded. â€Å"His place is with his own, or with the women at best!† â€Å"Hold to faith, Heafstaag,† Beorg explained. â€Å"‘This is deBernezan, a man of great import to our victory. Valuable is the information he has brought to me; for he has dwelt in Ten-Towns for two winters and more.† â€Å"Then what role does he play?† Heafstaag pressed. â€Å"He has informed,† Beorg reiterated. â€Å"That is past,† said Heafstaag. â€Å"What value is he to us now? Certainly he can not fight beside warriors such as ours.† Beorg cast a glance at deBernezan, biting back his own contempt for the dog who had betrayed his people in a pitiful attempt to fill his own pockets. â€Å"Plead your case, southerner. And may Tempos find a place in his field for your bones!† deBernezan tried futilely to match the iron gaze of Heafstaag. He cleared his throat and spoke as loudly and confidently as he could. â€Å"When the towns are conquered and their wealth secured, you shall need one who knows the southern marketplace. I am that man.† â€Å"At what price?† growled Heafstaag. â€Å"A comfortable living,† answered deBernezan. â€Å"A respected position, nothing more.† â€Å"Bah!† snorted Heafstaag. â€Å"He would betray his own, he would betray us!† The giant king tore the axe from his belt and lurched at deBernezan. Beorg grimmaced, knowing that this critical moment could defeat the entire plan. With his mangled hand, Heafstaag grabbed deBernezan’s oily black hair and pulled the smaller man’s head to the side, exposing the flesh of his neck. He swung his axe mightily at the target, his gaze locked onto the southerner’s face. But, even against the unbending rules of tradition, Beorg had rehearsed deBernezan well for this moment. The little man had been warned in no uncertain terms that if he struggled at all he would die in any case. But if he accepted the stroke and Heafstaag was merely testing him, his life would probably be spared. Mustering all of his willpower, deBernezan steeled his gaze on Heafstaag and did not flinch at the approach of death. At the very last moment, Heafstaag diverted the axe, its blade whistling within a hair’s breadth of the southerner’s throat. Heafstaag released the man from his grasp, but he continued to hold him in the intense lock of his single eye. â€Å"An honest man accepts all judgments of his chosen kings,† deBernezan declared, trying to keep his voice as steady as possible. A cheer erupted from every mouth in Hengorot, and when it died away, Heafstaag turned to face Beorg. â€Å"Who shall lead?† the giant asked bluntly. â€Å"Who won the challenge of the song?† Beorg answered. â€Å"Well settled, good king.† Heafstaag saluted his rival. â€Å"Together then, you and I, and let no man dispute our rule!† Beorg nodded. â€Å"Death to any who dare!† deBernezan sighed in deep relief and shifted his legs defensively. If Heafstaag, or even Beorg, ever noticed the puddle between his feet, his life would certainly be forfeit. He shifted his legs again nervously and glanced around, horrified when he met the gaze of the young standard bearer. deBernezan’s face blanched white in anticipation of his coming humiliation and death. The standard bearer unexpectedly turned away and smiled in amusement but, in an unprecedented merciful act for his rough people, he said nothing. Heafstaag threw his arms above his head and raised his gaze and axe to the ceiling. Beorg grabbed his axe from his belt and quickly mimicked the movement. â€Å"Tempos!† they shouted in unison. Then, eyeing each other once more, they gashed their shield arms with their axes, wetting the blades with their own blood. In a synchronous movement, they spun and heaved the weapons across the hall, each axe finding its mark in the same keg of mead. Immediately, the closest men grabbed flagons and scrambled to catch the first drops of spilling mead that had been blessed with the blood of their kings. â€Å"I have drawn a plan for your approval,† Beorg told Heafstaag. â€Å"Later, noble friend,† the one-eyed king replied. â€Å"Let tonight be a time of song and drink to celebrate our coming victory.† He clapped Beorg on the shoulder and winked with his one eye. â€Å"Be glad of my arrival, for you were sorely unprepared for such a gathering,† he said with a hearty laugh. Beorg eyed him curiously, but Heafstaag gave him a second grotesque wink to quench his suspicions. Abruptly, the lusty giant snapped his fingers at one of his field lieutenants, nudging his rival with his elbow as if to let him in on the joke. â€Å"Fetch the wenches!† he commanded. How to cite The Crystal Shard 3. The Mead Hall, Essay examples