VaR和RBC的差別主要在於風險相關性的結構，RBC以人為的方式設定風險之間為完全相關或完全無關，而VaR則經由歷史資料估計得到相關性的結構，當然也可能因估計的誤差而造成錯誤。

本篇文章的目的為探討相關係數矩陣對於資本需求的設定是否會造成影響，我們將利用產物保險業的資料來作模擬分析，並觀察資本需求制度因為相關性結構的設定是否會影響其效率及有效性。

我們將建立一個模擬中的世界，在這個世界中，產險公司將面臨股票投資風險、利率風險和核保風險等三種風險並根據1999年底美國產險公司的平均值來設定一個起始的保險公司的財務分配狀況，經過模擬後，利用兩種比較標準來比較類似RBC和類似VaR的資本需求，第一種標準為在監理上要求某種程度的型一誤差下所造成的型二誤差，第二種為資本需求的有效性，是否能在面臨相同的破產風險下，要求較低的資本。

我們的結果可以看到因資料點的增加，使得估計誤差減少，但VaR卻未因此而此RBC來得好，經過對股票的市場價值、債券的市場價值和負債三個部位作簡單的分析發現VaR和RBC兩者問的關係約為一個近似於1的比例，而此比例會因假設的相關係數矩陣而改變。因此，當監理機關在選擇監理的制度時，是否估計相關係數矩陣並不會有太大的影響，因為對於相關性作不同假設約兩種制度之間為一個近似於1的比例。

The major difference between risk-based capital (RBC) and value at risk (VaR) is the specification of the correlation structure among risks. RBC subjectively specifies that risks of insurers are either independent of each other or perfectly and positively correlated. Although VaR attempts to capture the underlying correlation structure through estimation of historical data, it is subject to estimation errors. The purpose of this paper is to examine how the mis-specification or mis-estimation of correlation structure affects the effectiveness of capital requirements in the property-casualty insurance industry.

We first construct a representative insurer in a simulated world with stock market risk, interest rate risk, and underwriting risk. RBC-type and VaR-type of capital requirements are then calculated as the financial status of the insurer evolves. All parameters in the simulation are based on historical data to approximate the real world. We then examine the effectiveness of these two capital requirements in terms of their early warning capabilities and the levels of capital needed for various solvency rates.

Our results show that the correlation estimation when using annual data has too big errors to bejustified. The capital requirement incorporating estimated correlation matrix was dominated by the one lacking correlation estimation. RBC-type requirement has lower chances to signal false alarms given the desired early warning capabilities and demands less capital for the same solvent probabilities. Insurance regulators therefore should not embrace correlation estimation into capital requirements before they could have insurance companies reported data more frequently.

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