Financial analysts

Tracking Error

admin — Sun, 04 Jul 2010 08:35:50 +0000

Just as corporations have to deal with “forecasting error” in terms of the deviation of forecast exchange rates relative to the actual future rate, so investors have to deal with “tracking error” within their portfolios, which is the return of the portfolio relative to the investment benchmark index being used. Within this, there is “expected” and “realized” tracking error. Expected tracking error is as the name suggests determined before the fact — ex ante — whereas the realized tracking error is determined after the fact.
Determining the relevance of tracking error is also a function of comparing the portfolio’s hedging strategy with a random strategy, which creates hedge/don’t hedge signals with equal probability on a regular basis. Using polar benchmarks — i.e. 0% or 100% hedged — the equal probability of the outcome of the random strategy suggests that hedge deviations will be zero in half the cases and 100% in half the cases. However, with a partially hedged currency benchmark, the deviations will vary in direct proportion to the ratio of the benchmark. For instance, for a symmetrical or 50% hedged currency benchmark, the deviations will be 50% from each side of the benchmark.
From this, we can gather two things, firstly that the tracking error — or the deviation — is a function of the hedged ratio used for benchmarking and secondly that the tracking error for a partially hedged benchmark should be less than that for a polar benchmark. Indeed, generally, the tracking error for a symmetrical or 50% currency hedging benchmark should be around 70% of the tracking error using polar benchmarks. Expressed differently, the tracking error of a polar benchmark should be 1.41 (square root of 2) times higher than that of a 50% hedged benchmark. The advantage of a symmetrical or 50% currency hedged benchmark for a portfolio manager is that it reduces the tracking error of the portfolio and also enables them to participate in both bull and bear markets compared to the polar benchmark where the participation is limited to either/or.
Tracking error can be further reduced by a technique known as “matched hedging”, which increases or decreases the hedge ratio relative to the change in asset allocation. Historically, the act of asset allocation itself within fixed income portfolios has been a major and seemingly unavoidable factor in increasing a portfolio’s tracking error. Matched hedging can reduce though clearly not eliminate this.
Tracking error can also occur under passive currency management. This is because in order to implement a passive currency hedging programme a portfolio manager still has to adjust the amount of the currency hedge relative to the value of the underlying as it changes on a regular basis — i.e. once a month. In reality, many portfolio managers don’t bother to do this. As a result, the residual that is left over- or under-hedged contributes to the tracking error. In this, the portfolio manager has to balance the transaction costs of re-balancing the currency hedges against the negative effect on tracking error.

Preparing Yourself for the World of Investing

admin — Thu, 10 Jun 2010 14:54:38 +0000

Bulls, bears, stocks and bonds. Many people enjoy the notion of saying that they are investors, but few are actually prepared to invest in the right way. Investing is like a boxing match in that there must be adequate preparation and training before a boxer ever steps into a gym. Like a boxer, an investor has to seek the right investment advice because they have much to lose if they are ill trained before the main event.

Before You Invest

Prior to investing, you should prepare for it by getting your finances in shape. First, you should be aware of your debt levels. There is no such thing as good debt but some types of debt are acceptable such as a mortgage loan. You need to get rid of any extra debt you have before you ever invest.
The reason is simple: if you invest, you may not earn enough to offset the interest being charged on your debt, and even worse you could lose your investment as well. For example, if you’re paying 6% interest on a student loan, you would have to earn over 6 percent on your investment returns in order to justify not concentrating on your debt load first.
After ridding yourself of debt, you need to build an emergency fund. If you lose your job or run into unexpected expenses like medical bills or your old car breaks down, you will be covered. Before trying to make money by investing you should have adequate savings to keep you going when emergencies occur.

Doing Research

There are all kinds of great investments for you to try out, but when starting out you should pick one and dedicate yourself to learning as much as possible about it. For instance, if you choose to invest in the stock market you should be reading as much as possible about it daily. Next, you should try a virtual stock exchange where you’re given fake money to invest. Try out various investment theories and see which one suits your style and risk tolerance most. There is really no right answer, but the wrong answer is to go in without training.
Remember that you can always start out with more simple investments like CDs or bonds before trying your hand at the stock market. Countless investors lose money because they are not ready for the dedication necessary serious investing. Don’t let yourself be unprepared when risking your money.

The No-Debt Vow

admin — Sun, 23 May 2010 16:11:33 +0000

The No-Debt Vow

Everybody always asks me what the first step to getting out of debt is, and the answer is always the same — stop digging. If you have already put yourself in a very deep hole, the only way to start getting out of that hole is to stop digging. Debt reduction may seem like a tricky thing, but in many aspects it is not. If you are serious about getting out of debt and beginning to live a financially responsible life, you have to kill all bad habits before you can begin to heal the wounds.

So if you have made the no-debt vow, how do you force yourself to stick to this regimen? Well look at it as if it was a diet, as if you are trying to reduce the amount of debt in your financial meals every day. The extra debt you have added on by irresponsible spending and gorging you must now eliminate by frugal spending and wise expenditures. Fancy gadgets and expensive toys will pop out of nowhere to tempt you, but it is up to you to fight such temptations and limit the amount of money you spend.

Now what is the best way to avoid these temptations? Well in many aspects it is impossible because we don’t always know where these temptations will come from. However, sometimes we do. Therefore we must find a way to limit our exposure to the things that we know are weaknesses for us, meaning things we know we have a soft-spot for and may end up costing us. If you are able to limit your own exposure to such items you are limiting the possibilities of you relapsing and adding to your debt collection.

Long-term Positions

admin — Sun, 15 Nov 2009 08:55:02 +0000

Positions that are of longer term are more often hedged through swap markets than forward markets. The structure of a foreign currency swap is very similar to that of a floating rate interest rate swap. We will take the case of a floating rate ¥1000bn five-year loan with interest paid every three months. In order to hedge the annual interest payments we would enter into a yen–dollar swap agreement with terms as follows: Nominal values of the contracts are ¥1000bn and $1bn. The amount to be paid by the yen payer is set at the current spot yen 90-day interest rate for settlement 90 days after.
The amount to be paid by the US$ payer is set at the current US$ 90 day interest rate for payment 90–days after.
Interest rate parity ensures that the US-based bank has fully hedged the interest payments due from the loan. (This is a simplified example and in practice we would have to look more fully at the pricing basis and payment terms of the loan and take these into account.)
The following, slightly more complex, worked example is of a three-year euro–yen swap. The conditions of the two parties are as follows:
Nominal value. Nominal values of the contracts are ¥500bn and €600m.
Payment calculation. Interest to be calculated on a quarterly basis. Payments by the yen payer are to be based on the spot yen 90-day London interbank rate plus 150 bpts and at the spot euro LIBOR for the euro payer. On the day that the agreement starts the two payments due are calculated based on 90-day yen rates of 0.75% and euro rates of 2.25%, giving payments due of ¥281.250m nd €3.375m.
Settlement. Settlement is to be made 90 days after the date of calculation on a netted basis in US$. The calculated payments are converted into US$ based on the then yen:US$ spot rate of 99.50 and a euro:US$ spot rate of 1.205. The yen payment due is US$2 826 633 while that of the euro payer is $2 800 830. The yen payer pays the difference of US$25 803 to the yen receiver.

GAP ANALYSIS

admin — Fri, 02 Oct 2009 08:53:11 +0000

In many countries banks are required to disclose their period-end interest rate gap positions in the form of the following report. These reports show balance sheet assets and liabilities broken down by when they are next due for repricing. The effects of off-balance sheet items such as swaps are also included within the summary.
A positive interest rate gap means that more assets than liabilities are due to be repriced in a particular time interval. The following bank has a negative yield gap over the next 12 months and as such net interest margins should benefit from falling interest rates.
This would suggest that we can quantify the impact of rate changes within a specific time interval. The impact of an increase in short-term rates for a specific interval is given in general by:
Impact on net interest income = Balance sheet gap for time interval × àr For the three-month or less time interval for a 100 bpt increase in rates would imply:
Impact on net interest income = ?($7500m × 0.01) = ?$75m
Concentrating on managing short-term interest rate gaps can help banks report relatively stable spreads but this may have the effect of ignoring duration gaps for assets and liabilities with long duration. This will lead to increased risks of losses in economic value.
In practice analysts do not find gap reports of much use for a number of reasons:
They represent a snapshot in time and by the time they are released are usually well out of date. They indicate how a bank was positioning itself for changing interest rates rather than what they are now expecting. The use of the off-balance sheet instruments allows banks to adjust their gap positions in the medium and long term relatively quickly. They do not take any account of embedded options whether explicit as with mortgage pre- payments, or implicit options that exist in many deposits. If interest rates rise some demand deposit holders will exercise their option to withdraw their funds and redeposit them in an interest-bearing account. The time intervals are generally very broad and banks do not report an average repricing period. An analyst usually makes simplifying assumptions, for example that all deposits in the three to six-month time frame are repriced after four and a half months. Interest rates can remain stable for a protracted period but at times may change on a regular basis over a period of many months. It becomes increasingly difficult to estimate the potential impact of multiple interest rate changes on repricing. Rates across the yield curve do not usually change in parallel.
Banks are not passive observers. When interest rates are falling they will try to cut borrowing rates more than they cut lending rates. Lending rates are generally relatively sticky in a falling interest rate environment.

EMERGING MARKETS AND CURRENCY HEDGING

admin — Mon, 06 Jul 2009 08:37:42 +0000

It has been noted that emerging markets have different market properties to those of the developed markets. Here, it is important to sell these out and then in turn relate them to the considerations of passive and active currency risk management. First off, let us look at the major differences that appear present in emerging markets:
Liquidity risk — Emerging market currencies are less liquid than their developed counterparts. For instance, every day some USD300 billion goes through EUR–USD. This compares with around USD10 billion daily in the South African rand. Needless to say, this lower liquidity affects pricing and price action.
Convertibility risk — Even less than liquidity risk, convertibility risk is not a consideration for developed currency markets as all major currencies are freely floating and fully convertible. A number of emerging market currencies however are still not convertible on the capital account, and indeed a few are still not fully convertible on the current account.
Exchange controls — In line with this, several emerging market currencies still have varying degrees of exchange rate controls, which also distort exchange rate pricing and economic activity. Exchange controls create “black market” activity and paradoxically can lead to capital flight.
Emerging markets have structurally high levels of inflation — Stronger growth levels and economic inefficiencies are important reasons behind structurally high levels of inflation relative to developed markets. This in turn means that policy interest rates are in most cases substantially higher in emerging markets than in developed markets, resulting in high forward premiums.
Capital inflows however can depress market interest rates — The size of global capital flows relative to the size of local capital markets in most emerging markets can mean that the latter are swamped by a relatively small portfolio shift in assets either into the market or out of it. As a result, interest rate volatility is a lot higher.
Forward rate bias is lower in emerging markets — While forward exchange rates are poor predictors of future spot exchange rates in the developed markets, this is less so in many emerging markets. The exhaustive 2000 study by Bansal and Dahlquist tested the presence of forward rate bias and found emerging market currencies show significantly less correlation between current interest rate differentials and subsequent spot returns than those in the developed markets. That said, emerging market currencies tend to appreciate on a real basis and then collapse to adjust for the trade balance deterioration caused by that real exchange rate appreciation.
Implied emerging market volatility below developed market volatility is a buy signal —
Historically, lower levels of implied volatility in emerging market currencies than the corresponding developed market currencies has proven a good buy signal for the former. Intuitively, emerging market volatility should be higher, though there are periods when the sheer weight of capital inflows forces it artificially lower. Note that emerging market implied volatility is skewed in that it tends to fall only when the emerging market currency is strengthening, but always rises when the currency weakens.
Implied emerging market volatility is a very poor predictor of future exchange rates —
Looking at previous emerging market crises, the options market has usually got it “wrong” in the sense that such crises have never been priced in ahead of time by the options market. Thus, we can say that the options market is a poor predictor of future exchange rate levels in the emerging markets, though measured against historic volatility levels it may well be a much better indicator of relative value.
What we find in the emerging markets is that shifts in global capital flows have major domestic interest rate implications. For instance, high inflation and therefore interest rate differentials should, according to classical economic theory, suggest a depreciation of the local currency in proportion to that interest rate differential or forward premium. However, this may not occur due to heavy capital inflows, which swamp the domestic market’s ability to cope with these without economic distortion. As a result of this, the currency may experience significant nominal and real appreciation, in seeming violation of the international Fisher effect and covered interest rate parity. Real currency appreciation however leads to a real economic shock, and more specifically real trade and current account balance deterioration. Eventually, this has to be reversed and not too surprisingly through real currency depreciation. The longer and more powerful the real appreciation, the potentially more violent the subsequent depreciation. Emerging market currencies trade in these types of cycles, in line with the “speculative cycle” that we looked at earlier in the blog. As a result, we can tell from this that the forward rate bias is extreme for emerging market currencies on both sides of the forward. In line with this, some caution is needed in using the differential forward strategy in the emerging markets. Emerging market interest rate differentials would mean theoretically that an investor never hedged emerging market currency risk using the differential forward strategy, yet this is clearly not the appropriate strategy in some cases.
For similar reasons, the carry trade has provided significant alpha for active currency managers, both in the basic and in the optimized version. However, the distortion to interest and exchange rates that capital inflows provide in emerging markets means that a significantly higher degree of both care and discretion is needed in picking higher carry currencies to either invest in or hedge depending upon the reading of the risk appetite indicator.

Optimization of the Carry Trade

admin — Sun, 05 Jul 2009 08:36:58 +0000

The final strategy example that we will look at for active currency managers is that of optimizing the carry trade. We looked at the carry trade idea initially in earlier posts and will do so again in the nest few posts in the context of an appropriate strategy for currency speculators, when using a risk appetite indicator, for the purpose of gauging when are the best and worst times to buy higher carry currencies (and thus go short the lower carry currencies).
This combination of a risk appetite indicator and a basket of higher carry currencies can also be used for the purpose of currency hedging by an active currency manager who trades and hedges currency risk around their benchmark. For a currency speculator, the principle of the risk appetite/carry trade combination is that the basket of higher carry currencies should be bought when the risk appetite indicator is in either risk-seeking or risk-neutral mode and should be shorted when it is in risk-aversion mode. Similarly, the currency hedger could use this combination of indicators to go underweight the hedge relative to the benchmark in higher carry currencies when the risk appetite indicator is benign and overweight when the indicator moves into risk aversion. Such a strategy should reduce transaction costs relative to a passive currency management programme, while also reducing the portfolio’s overall risk and adding alpha.
Yet, we can fine tune this strategy still further using a portfolio optimizer to take into account the volatility and correlation of currencies in addition to their yield differentials alone. This should both in theory and practice produce better returns than the simple carry trade strategy. The carry trade can be an excellent strategy by itself for adding alpha, however it can also exhibit substantial volatility at times. A fine example of this was when the dollar–yen exchange rate fell by around 15% in the space of a few days in October 1998. By comparison, the optimized carry trade would in the case of the currency speculator represent the buying of higher carry currencies with low volatility and the selling of low carry currencies with high volatility. For the currency hedger, this would in turn mean going underweight the hedge relative to the benchmark on higher carry currencies with low volatility and overweight the hedge on lower carry currencies with higher volatility.
For both a portfolio manager who is looking to hedge currency risk and an active currency manager who can trade that currency risk, optimizing the carry trade can be a useful and productive way both to reduce risk and to add alpha. Indeed, it is an improvement on the differential forward strategy in so much as that is another expression of a basic carry trade strategy. The optimized carry trade strategy has consistently produced good returns with of necessity less volatility, resulting in higher Sharpe and information ratios.
It should of course be noted that just as one can optimize the carry trade for improved performance over the simple carry trade, so one can do exactly the same thing for either the differential forward strategy or the trend-following strategy. One does this by looking at volatility-adjusted exposure rather than the simple exposure per se. Thus, for example in the case of the differential forward strategy, one can over an extended period of time look at the relationship between implied volatility and historical volatility of the underlying exchange rate. Optimizing for volatility-adjusted exposure, the active currency manager would increase the leverage of the forward hedge when implied vol is below a predetermined threshold relative to historic vol at the same time as the forward points are in favour of the hedger, and conversely lower it when implied vol is above. The extent to which this generally improves performance far exceeds any concerns about increased transaction costs. One thing which may have to be taken into account however is the likelihood that raising or lowering the leverage of a differential forward strategy, both on an absolute basis and relative to the benchmark, may have an impact on the volatility of the tracking error.
Similarly, one can seek to optimize through volatility-adjusted exposure the trend-following strategy. Again, this should improve on the alpha provided by the basic strategy. A final point on these active currency strategies is that they are obviously not dependent on the base currency for adding alpha given that the total portfolio weighting and risk remains the same whatever the base currency.

Adding “Alpha”

admin — Fri, 03 Jul 2009 08:34:47 +0000

The motive of risk reduction is primarily defensive, in that it seeks to defend or maintain the portfolio’s return within a given tolerance of overall risk. That for adding “alpha” on the other hand is quite different, in so much as “alpha” refers to the excess return generated by an active currency manager relative to a passive hedging programme.
Economic theory suggests that the long-term return of a currency is zero, so how can an active currency manager add value or “alpha”? There appear to be two aspects to this question. Firstly, currency markets are dominated by short-term movement. Thus, while their long-term return may be zero, their short-term returns (and losses!) may be significant. Secondly, it should be remembered that the same theory that suggested there were fundamental equilibrium levels for currencies also suggests that their long-term returns are zero. While not rejecting such a theory outright, it should surely be treated with some care, put in this context.
Indeed, there is a fine — and increasing — body of academic work that suggests that contrary to theory, managing currency risk can indeed add “alpha”. Among these, I will draw out several notable examples. Firstly, while formulating his “Universal Hedging Policy” in 1989, Fisher Black suggested that currency was, contrary to theory, not a zero sum game and investors could indeed increase their returns by holding currency inventories. Needless to say, this contradicted the widely held view that currencies could not provide added value because currency markets were perfectly efficient. A relatively short time after that, Mark Kritzman put forward the view that active currency managers could take advantage of the apparent serial correlation in currency returns. Subsequent research by Taylor (1990) and Silber (1994) targeted market trends as being behind persistent positive returns from currency managers.
Two further research reports that should be mentioned are those by Strange (1998, updated 2001) and The Frank Russell Company (2000). In the first case, the survey by Brian Strange, as published in Pensions and Investment (15/6/98), entitled “Do Currency Managers Add Value?” stated that of the 152 individual currency overlay programmes managed by 11 firms, these produced an average of 1.9% per year over a 10-year review period from 1988 to 1998, while simultaneously reducing the risk of the portfolio. In other words, not only did currency managers consistently add value, but their action of seeking to manage currency risk also helped lower the overall risk profile of the portfolio, thus boosting the Sharpe ratio from both sides! The second example is that of the Frank Russell study of May 2000 entitled “Capturing Alpha through Active Currency Overlay”, which analysed the historical performance of currency overlay mandates and confirmed the view that managing currency risk does indeed add value or “alpha”.
As noted above, a host of empirical studies have proven conclusively that active currency management can indeed boost the portfolio’s return, both on an absolute basis and in this context relative to not hedging, in contrast to classical exchange rate theory. In line with this, a number of studies have been published suggesting clear market inefficiencies, which might therefore be taken advantage of by active currency managers. For instance, the 1993 study by Kritzman, suggesting that the discount/premium of the currency forward contract “systematically and significantly overestimated the subsequent change in the spot rate”. Kritzman also introduced the concept of so-called “bilateral asymmetry”, referring to a bias by risk-averse investors for the perceived predictable returns of the interest rate differential as opposed to the unpredictable returns of the currency. Work by Choie (1993) supported these findings. Overall, a body of informed opinion has developed, supportive of the view that active currency management can add value.
After finally admitting that currency markets may offer profit potential, whether over the short or long term, academic theorists have suggested that such profit opportunities may exist in currency markets because there are some currency market participants that are not solely or even mainly motivated by profit. Classical theory suggests rational currency market participants are solely profit-seeking and moreover offset each other, with the result that any outstanding profit opportunities are instantly arbitraged away. Thus, from this, they seek to explain the existence of sustained profit opportunities within currency markets by suggesting that non-profit-seeking currency market participants such as central banks, tourists and national or corporate Treasuries effectively distort pricing. To me, such a view appears more reflective of the guesswork of someone who does not actually know the answer but is afraid to own up. Currency markets generate profits because it is the theory that they should not that is wrong rather than the currency market itself.
Active currency management can add value because there is value to be had in currency markets, plain and simple. Within this, an active currency manager will clearly favour the most flexibility possible to add that value, both in terms of the currency benchmark that they have to operate under and the currencies and financial instruments with which they are allowed to trade. For the active currency manager, the foreign currency return is not just a matter of currency translation of the underlying asset, but also of the excess return or alpha that the currency manager is able to add. The alpha an active currency manager generates is usually measured against an unhedged position. However, probably a truer idea of the alpha the active currency manager generates would come from comparing their returns to those of a passive currency management strategy of maintaining the benchmark hedge ratio. Historically, the typical mandate has allowed managers to vary the hedge ratio between 0 and 100% regardless of the benchmark.

HEDGING — MANAGEMENT RELUCTANCE AND INTERNAL METHODS

admin — Thu, 02 Jul 2009 08:34:45 +0000

Having looked in detail at the issue of managing currency risk, we should now be looking at the specifics of how to hedge that risk. Before we do that, we first have to examine the issue of management reluctance to hedge a risk many see as merely an operational hazard of international investment. Some may dismiss this section, either because it is irrelevant to them or because they view any such approach as inappropriate. While I too share the view that currency risk should be managed, such management reluctance should not be ignored, but instead should be understood and thereafter combated. Three key reasons for this reluctance which come up time and again are the following:
Management does not understand active currency management methods
Management thinks currency risk cannot be measured accurately
Management sees active currency management as outside of core business
Some of these points are reasonable. Currency forwards and options may well be outside the field of expertise of a corporation’s management, and will certainly be outside the core business operations. Many managements consider such financial instruments as speculative. However, it is the job of Treasury to explain that not managing currency risk actively leaves the corporation vulnerable to major exchange rate movements, which can cause substantial swings in the company’s value. Using forwards or options may indeed be speculative, depending on what they are used for. However, not hedging currency risk may be even more speculative. Active currency management is a necessary byproduct of a corporation’s overseas investments and operations. Again, it is the job of the Treasury to educate the management and ultimately the board on the need for active currency management, not least to maintain and ensure the corporation’s equity market value. A corporation may not be able to boost shareholder value significantly through active currency risk management, but it can certainly damage it by not managing currency risk.
When management says it is difficult to measure currency risk it is correct, but that does not mean such risk cannot be quantified. Imprecision is not an excuse for indecision in the corporation’s underlying business. Neither should it be tolerated with regard to currency risk management.
Even if a management is willing to consider currency hedging, there are ways of “natural” or internal hedging that it may consider first, such as:
Netting (debt, receivables and payables are netted out between group companies)
Matching (intragroup foreign currency inflows and outflows)
Leading and lagging (adjustment of credit terms before and after due date)
Price adjustment (raising/lowering selling prices to counter exchange rate moves)
Invoicing in foreign currency (this cuts out transactional exposure)
Asset/liability management (for balance sheet, income or cash flow exposure)
Netting involves the settling of intragroup debt, receivables and payables for the net amount. The simplest form of this is bilateral netting between two affiliates.
Matching is similar but can be applied both to intragroup and third-party flows. Here, a corporation “matches” its foreign currency inflows and outflows with respect to amount and timing.
Leading and lagging refer to adjusting credit terms between group companies, where “leading” means paying an obligation in advance of the due date and “lagging” means after the due date. This is a tactic aimed at capturing expected currency appreciation or depreciation. Price adjustment involves increasing selling prices to counter exchange rate moves. Invoicing in foreign currency reduces transaction risk relating specifically to exports and imports.
Asset and liability management can be used to manage the balance sheet, income statement or cash flow exposure. Corporations can adopt either an active or a passive approach to asset and liability management, depending on their currency and interest rate risk management policy.
Finally one can hedge internally by increasing corporate gearing. Leverage shields corporations from taxes because interest is tax-deductible whereas dividends are not. However, the extent to which one can increase gearing or leverage is limited by costs. That said, if currency hedging reduces taxes, shareholders benefit.
For practical purposes, three questions capture the extent of a corporation’s currency risk:
1. How quickly can a corporation adjust prices to offset exchange rate impact on profit margins?
2. How quickly can a corporation adjust sources for inputs and markets for outputs?
3. To what extent do exchange rate moves have an impact on the value of assets?
Within a corporation, it is usually the case that those who can come up with the best answers to these questions are directly involved in such tasks as purchasing and production. Thus, finance executives who focus exclusively on the credit and currency markets can in fact miss the real essence of a corporation’s currency risk. Furthermore, the exact answers to these questions need to be known not only by the oversight or risk committee, but preferably by the CEO as well. If they don’t, they effectively don’t know both the value and the exposure of the corporation.